श्री रूद्राष्टकम् स्तोत्रम्
नमामीशमीशान निर्वाणरूपं
विभुं व्यापकं ब्रह्मवेदस्वरूपम् ।
निजं निर्गुणं निर्विकल्पं निरीहं
चिदाकाशमाकाशवासं भजेऽहम् ॥ १॥
निराकारमोंकारमूलं तुरीयं
गिरा ज्ञान गोतीतमीशं गिरीशम् ।
करालं महाकाल कालं कृपालं
गुणागार संसारपारं नतोऽहम् ॥ २॥
तुषाराद्रि संकाश गौरं गंभीरं
मनोभूत कोटिप्रभा श्री शरीरम् ।
स्फुरन्मौलि कल्लोलिनी चारुगङ्गा
लसद्भालबालेन्दु कण्ठे भुजङ्गा ॥ ३॥
चलत्कुण्डलं भ्रू सुनेत्रं विशालं
प्रसन्नाननं नीलकण्ठं दयालम् ।
मृगाधीशचर्माम्बरं मुण्डमालं
प्रियं शंकरं सर्वनाथं भजामि ॥ ४॥
प्रचण्डं प्रकृष्टं प्रगल्भं परेशं
अखण्डं अजं भानुकोटिप्रकाशम् ।
त्रयः शूल निर्मूलनं शूलपाणिं
भजेऽहं भवानीपतिं भावगम्यम् ॥ ५॥
कलातीत कल्याण कल्पान्तकारी
सदा सज्जनानन्ददाता पुरारी ।
चिदानन्द संदोह मोहापहारी
प्रसीद प्रसीद प्रभो मन्मथारी ॥ ६॥
न यावत् उमानाथ पादारविन्दं
भजन्तीह लोके परे वा नराणाम् ।
न तावत् सुखं शान्ति सन्तापनाशं
प्रसीद प्रभो सर्वभूताधिवासम् ॥ ७॥
न जानामि योगं जपं नैव पूजां
नतोऽहं सदा सर्वदा शम्भु तुभ्यम् ।
जरा जन्म दुःखौद्य तातप्यमानं
प्रभो पाहि आपन्नमामीश शम्भो ॥ ८॥
रुद्राष्टकमिदं प्रोक्तं विप्रेण हरतोषये ।
ये पठन्ति नरा भक्त्या तेषां शम्भुः प्रसीदति ॥

In this part, we will see detailed meaning and word by word explanation.
First, Rudrashtakam start from 'Namami' which shows, I honour to. It also indicate that we are free from ego because to give respect to someone, one shouldn't have ego.
After Various Names of Lord Shiva shown which explain glories of Mahadev.
It says, 'Isha Ishana' means who is God of Ishana direction (It is between north and east). Location of Himalaya is in this direction from the India.
'Nirvana roopam' tell, Shiva is form of complete peace, eternal happiness who is beyond world's sorrows. Everyone in world is incomplete. Only Lord Shiva is complete.
After stotra call Shiva by names 'Vibhu', 'Vyapaka', 'Brahman'. It glorify that Shiva is everywhere in world. They are in world and also beyond it. They are ultimate destination for all souls. They are Supreme who is not possible to define.
'Vedaswarupam' - One who is form of Vedas. Shiva has all knowledge. They know all Vedas and Puranas, nothing is in world that is unknown to them.
'Nijam' or 'Ajam', who is birthless, who have no origin. Shiva is also called as Swayambhu because they appear by themselves as they think.
'Nirguna' - One who is above all Gunas. There is Satvaguna, Rajoguna, but it is for material world. In this world, creatures are not perfect, and he has desire, ego, by which he trap in illusion of world. But God Shiva is perfect, who is not in control of Gunas.
Lord Shiva is 'Nirvikalpa', who is always as they are. They don't change. They are absolute, above all states, thinking.
'Niriham' - Shiva is free from desires. God Shiva is called as Vairagi, once they burn Kamadeva (Cupid), who try to generate desires in them.
'Chidakashmakash Vasam' - One who have cloth as sky. They have no body. They stay in everyone. They are in the world, and also not in it. We give honour to such God Mahakal, Shiva by saying 'Bhaje Aham'.
'Nirakar' - Shiva is shapeless, formless who is also creator of all things we see. They also create shape, size, colour.
'Omkaramoolam' - source of Omkara. Om is fundamental, has all power and represent Supreme Brahman.
'Turiyam' - who is in state of consciousness, beyond deep sleep. Shiva is above all perception, feelings, and in stage for which no way to describe it.
'Giragyan Gotit misham' - Shiva can't known by any knowledge, they are above every physical phenomenon. They can't understandable by listening, touching or seeing. Process of visualization or seeing depends on electromagnetic wave which eyes detect and brain find patterns, try to make image. Due to blessing of Shiva, we get such extremely designed brain. How can we perceive Shiva in ego that we can see them by material things!
'Girisham' means Lord of mountain. In Sanskrit, 'Gir' means mountain and 'Ish' means Ishwara, God.
'Karalam' - Shiva is big who's form seems horrible. In first appearance, they seem with Ash, skin of tiger, with snakes, which can seem terrible to one who not know symbolism behind it. Once Mena, mother of Goddess Parvati, shocked by seeing Lord Shiva in this form, but as she knows reason, she give hand of Parvati to Mahadev.
'Mahakalakalam' - Shiva is beyond time, beyond death. In ancient history, there is numerous occasions when Shiva protect devotees from death, Yama.
'Krupalum' - Shiva has kindness like sea. They forget mistakes of Jeevas (creatures), and save him from dangers.
Lord Mahadev is 'Gunagar', who's glories and qualities never ends. Thousands and thousands of scriptures can't explain. Even Goddess Saraswati sing qualities for crores of years, there is still nothing really can explained. Shiva is infinite, and have infinite sea of qualities.
'Samsaraparam' - one who above material world, who helps devotees to cross trap of world.
I give honour to Lord Shiva by saying 'Natoaham'.
'Tusharadrisankash Gauram' - Shiva's appearance is like mountain which covered by snow. Their thoughtfulness is described by 'Gambhiram'.
'Manobhoot Koti Prabhashri Shariram' - Who's such that crores of rays spread from their body, crores of Cupid seems nothing towards them.
'Sfuranmauli kallolini charu ganga' - from who's hair, flow of holy Ganga comes on Earth. Ganga comes on head of Shiva by Penance of Bhagiratha and his ancestors. It's flow is so dangerous that Earth can't resist it, and therefore Lord Shiva adopt it in hair.
'Lasadbhal balendu' - On who's head a crescent Moon is there. Shiva save moon from curse of Daksha. Moon and other sages chant Mahamrityunjay mantra 10 crores times in Prabhasa, and pleased by it, Lord Shiva make curse such as he fifteen days he will rise and in fifteen days he decay. In a form when moon is decay or crescent, Shiva give him place on Head, and therefore also known as Chandrashekar.
'Kanthe Bhujanga' - who have snake on neck. Shiva controlling snakes indicates, they are controller of horror, dangers.
'Chalat Kundalam' - Who wears celestial ear rings
'Bhrusu netram vishalam' - Who's eyes is divine, big. Shiva have three eyes. To destroy evils, they open third eye. It is also Symbol of knowing past, future and present. They also known as Trayambak.
They have also destroyed Kamadeva by third eye.
'Prasannananam' - Who is happy, who's face is happy. By remembering whom, devotee get peace, who take away every sorrow of devotee. Their face is unimaginable, their form is not just one, but so many. In which form devotee pray, they take that form.
'Nilakantham' - Who have throat of blue color. There is interesting history behind name. Once in Samudramanthana, poison comes out. No one able to shallow it, except Lord Shiva. To save universe and to mercy on everyone, Shiva drink poison. They drink in way that it don't fall below throat. They hold it in throat. By effect of poison, and actually divine play of Shiva, color of throat becomes like blue. In Sanskrit, 'Nil' means Blue and who have blue 'Kanth' - throat, is Nilakanth.
'Dayalam' - Who is kind. Who's kindness is endless. Whenever devotee face problem,they instantly remove it. They reduced curse on moon, and give him place on head. They save universe from poison. Devotees who gives just water on Shivling, they give enormous wealth. They are remover of sorrow, ego, illusion.
'Mrugadhish Charmambaram' - Who have cloth of animal skin, skin of elephant and skin of tiger. Shiva wear skin off elephant because it is asked by Gajasura. What exact happens? Once, Gajasura has a boon from he can't killed by anyone who is affected by lust. He understands himself as immortal, and in ego, he destroy numerous place. To save everyone, Lord Shiva fight against him. As Shiva is free from desire, they end Gajasura's life. While he was dieing, he ask a wish to wear his skin. Shiva fulfill it and from then they also wear skin of elephant.
'Mundamalam' - Who has skulls in neck. In event of Lingodbhava, Brahma lie, and Kalbhairava cut the fifth head of Brahma. Cutted head of brahma is weared by Shiva.
'Priyam shankaram' - Who's beloved by devotee, Shiva, Shankara. Shiva has crores of devotees, they are always in heart of devotee.
'Sarvanatham' - Who's Lord of everyone. Even one is Devtas, human or demons, Shiva is Lord of all. They protect animal, they give enough to every creatures. I honour to such Shiva by 'Bhajami'.
'Prachandam' - Who's furious, angry. Shiva is angry for evils, for who harms other. Shiva's angry form is in Durvasa Avatar in which they have anger to test devotee.
'Prakrushtam' - Who's transcendent, best, without limits. Shiva is incomparable, God of animal, all Jeevas. They present in Universe still they are not there. They are infinite and beyond Infinity.
'Pragalbham' - Who's strongest, brilliant.
'Praresham' - Who's Highest God, Who's Highest soul, for whom every soul originated, and come back in to them in end.
'Akhandam' - Who's complete. Who's always in whole form. Without whom, world is incomplete, without who's devotion, soul trapped in material world. Who's original destination for all soul, by who's mercy creatures be a whole.
'Ajam' - Who have no birth. Who's eternal, reason for origin of all.
'Bhanukoti Prakasham' - Who shine like crores of sun. In fact, there is no way to measure Shiva's brightness. They are brighter than most brightest star in galaxies. Even brightness not explain their form, they are above photon particles which is reason for emiiting and transmitting light. But still if Shiva want to take form, they are brighter than crores of sun, and combination of all source of light.
'Trayashul Nirmulanam' - Who remove three types of sorrow. As per Scriptures, sorrows are of three types named, aadhi, vyadhi, upadhi. But Shiva is remover all problems from life of devotee, even it is related to the mental problem, health, any pain, or any types of problems. Shiva also has Trishula in hand, which shows, they destroy all three sorrows.
'Shulapani' - Who has Trishula in Hand. Shiva has Trishula, which is one of the most powerful weapon. It has such power that if anything destroy by it, it will never come back to original place. Once due to deep reason, they cut head of Ganesha by Trishula. After request of gods, and Goddess Parvati, they join head but it is of elephant's head. Original head of Ganesha will not there, as it cutted by Trishula.
I honour to Shiva by 'Bhajeaham', who is 'Bhavanipati', husband of Goddess Parvati, who likes devotion and called 'Bhavagamyam'.
'Kalatit' - Who's beyond five elements. Who's above knowledge, who's not subjected to limitations.
'Kalyan' - Who's Auspicious one. Name Shiva also refer to one who's auspicious. They always want best of devotee, even he is demon. To protect world, and welfare of Universe, they even drink poison.
'Kalpantkari' - Who end Kalpas. Shiva ends our Universe, but it is not sign of ending forever, because each end has starting, and it start creation against. Creation and destroyance is cyclic process occurs each time, and one cycle is called Kalpa.
'Sada Sajjananandadata' - Who gives happiness to good people. People who works according to Dharma and always helps other, are liked by Shiva. Shiva provide him peace of mind, and happiness.
'Purari' - Who win over Tripurasura.
Once three demons penance on Brahma. When Brahma pleased, they first asked immortality. But Brahma denied and says, Anyone who takes birth have death. Ask anything else. Demons ask to live in city, and special location of sun, moon, Graha which occurs only one time in thousand year, at time who ends all cities by one arrow can only kill us. After Demons live in city. First they follow Dharma, but they create problem for heaven, and as they follow path of Dharma, they can't killed by anyone.
After due to illusion by Lord Vishnu, they stop following Dharma and take path of unrighteousness. As they leave Dharma, they able to be killed. After request of gods, Shiva ends city at specific combination of Graha.
Shiva destroyed city Tripura, so they are also known as Purari and Tripurari.
'Rudrashtakmidam Proktam Vipren Har Toshaye'
Means -
To please Lord Shiva one Brahmin speak this Stotram.
It show that Rudrashtakam is first chanted by Brahmin to get blessing from Shiva.
Tulsidas who is author of Ram Charit Maanas, write this Stotram. He is great devotee who also compose Hanuman Chalisa, a very famous prayer.
Second part of verses,
'Ye Pathanti Nara Bhaktya Tesham Shambhu Prasidati'
Who read Stotra with devotion, Lord Shiva pleased on him.

Chanting Rudrashtakam with devotion please God Shiva.
Who read this Stotram in morning and evening everyday, Lord Shiva become happy on him, and give blessing.
Anyone who read Stotram of Shiva even once in life, he still get effects. His sins reduced, and his mind move towards devotion.
He realized God Shiva and want to chant more mantras of Shiva.
One history of Mahashivratri signify chanting names or pouring water on Shivling unknowingly even give major benefits to Hunter.
Chanting Stotram fulfill material wish of us. But it is better if not ask anything from God. There is two types of devotion and, in which we don't ask anything from God, is best.
Moksha is not far, when we start to chant Stotram, and worship Lord Shiva.
Chanting names and mantras of Shiva make us like God Shiva, and their great qualities comes in us. God Shiva has so many qualities that thousands of years is too low to know it. Lord Shiva is very kind, who is outer than material things, they teach us that everything is temporary in world. They always meditate, which teach us that we should also meditate, and also numbers of scientific research prove that meditation has very deep effect on us. Everything about God Shiva is great, every symbol of them has special meaning.
Our Graha problem reduced. Stotram can solve astrological problems. By chanting Stotram, we become devotee of Shiva and Piplaad has given a boon that who is devotee of Shiva, will not face Shani Graha effect. One who believe in Shiva, worship them, are protected by them. God Shiva is called Mahakal, who win over death, who saved devotees from death. They will not face devotee a problem of Graha, Nakshatra.
Shiv Rudrashtakam helps to improve our spiritual growth. We can know more about Shiva. It describe form of Mahadev and omnipotent of them.
It fill power in us. Our mind become instantly fresh and tiredness go away.
It makes us stable, and strong. It has such effect which generate energy in us. We feel happiness, a ultimate happiness, not experience previously.
Any material things can't provide peace which is equal to Stotram dedicated to Shiva.