ॐ नमो भगवते रुद्राय॥ om namo bhagavate rudrāya ||

This does not form part of Vedic text. Like any other mantra, this verse also starts with om, which always gives auspicious beginning of all Vedic verses. Namo is the salutation to Rudra, like namaḥ. Bhagavate is derived from the word bhaga, which means gracious lord, good fortune, happiness, welfare, prosperity, dignity, majesty, distinction, excellence, beauty and loveliness. These are the attributes of Bhagavān or the Lord. Thus, a simple salutation is made to Rudra, at the time of beginning of Śrī Rudram seeking His Grace.

Vedic text begins from here.

नमस्ते रुद्र मन्यव उतो त इषवे नमः।

नमस्ते अस्तु धन्वने बाहुभ्यामुत ते नमः॥

namaste rudra manyava uto ta iṣave namaḥ |

namaste astu dhanvane bāhubhyāmuta te namaḥ || (anuvāka 1: verse 1)

Meaning:

Rudra! Salutations to your righteous wrath; your bow and arrow; to both of your hands. Again salutation to you.

Notes:

manyu does not mean just normal human anger. It specifically refers to the wrath of Rudra, which arises out of intolerance of adharma and evil doers. Rudra does not hesitate to punish wrong doers and incessant sinners. In His two hands, He holds a bow and an arrow. Bow and arrow symbolically represent aim of action and movement respectively. Rudra also means the one who causes pain and consequent pain. When adharma prevails, Rudra uses His weapons, bow and arrow to inflict pains on the wrong doers. Fearing His wrath, jīva-s always do good deeds. Rudra is like a master to us, ready to punish our wrong doings. There are reference to this interpretation in some of the Upaniṣad-s. Not only are His weaponries worshiped, but also His hands holding these weaponries.

या त इषुः शिवतमा शिवं बभूव ते धनुः।

शिवा शरव्या या तव तया नो रुद्र मृडय॥

yā ta iṣuḥ śivatamā śivaṁ babhūva te dhanuḥ |

śivā śaravyā yā tava tayā no rudra mṛḍaya || (1:2)

Meaning:

Your arrow which is the most benignant of all and your bow, which is the most auspicious and your quiver (a case for holding arrows) which is the source of blessings; make us happy with these.

Notes:

In the previous verse, jīva-s were frightened by His bow and arrows. In this verse, they are considered as auspicious and blessings. First, because He is worshiped along with His weaponries. Secondly, having understood that He will surely inflict pain if one continues with his sins, we are cautious in doing in any non-meritorious actions (papa) and avoid them somehow. In other words, when we surrender unto Him, we need not fear for Him. Surrender cannot happen all of a sudden. Surrender is possible only through a purified mind. Purified mind can never even think of following the path of adharma. When we follow the righteous path, there is no need for us to fear for Rudra. He becomes our Saviour.

या ते रुद्र शिवा तनुरघोरा अपापकाशिनी।

तया नस्तनुवा शन्तमया गिरिशन्ताभि चाकशीहि॥

yā te rudra śivā tanuraghorā apāpakāśinī |

tayā nastanuvā śantamayā giriśantābhi cākaśīhi || (1:3)

Meaning:

Though you are terrible one, your body is full of auspiciousness and non-freighting and destroy our sins. Reveal to us the path of Liberation (path to liberation is devoid of sins) by remaining at the top of Mountain (Mount Kailāśa). Giriśanta means inhabiting mountains. But this word is also explained as Supreme Knowledge, which is the path to mokṣa (emancipation).

Notes:

A subtle reference is made here to Shiva. According to Purāṇa-s, Shiva lives on the top of Mount Kailāśa. However, giriśanta is also interpreted as Supreme Knowledge or the one who imparts the knowledge of emancipation, as revealed by Upaniṣad-s. Brahman is both good and bad, as He is omnipresent. Similarly He does both good and bad to us, according to the impressions of past actions (karma). When karmic impressions are bad, we are bound to undergo sufferings, as Brahman never overrules His own law known as “Law of Karma”. We attempt to become His devotee by establishing a contact with Him through our mind. Therefore, the concept of God reflects our mental condition. When we think and act good, Rudra is good to us. On the other hand, if we transcend the rules of dharma, Rudra assumes a terrible form for us. The mere thought of Rudra removes all the sins, provided we are able to establish a strong connection with Him through our mind. Such a purified mind seeks His Grace for Liberation. This verse can also be considered as a prayer addressed to Purāṇic Shiva.

यामिषुं गिरिशन्त हस्ते बिभर्ष्यस्तवे।

शिवां गिरित्र तां कुरु मा हिसीः पुरुषं जगत्॥

yāmiṣuṁ giriśanta haste bibharṣyastave |

śivāṁ giritra tāṁ kuru mā hisīḥ puruṣaṁ jagat || (1:4)

Meaning:

O Lord of Mountains! The arrow you hold in your hand be an arrow for your blessings. Let your arrows not hurt any of the beings. You are the protector of all (the universe).

Notes:

Importance of attaining His Grace is emphasised repeatedly. Previous verses prayed for individual happiness and prosperity. This verse addresses the Lord for universal peace and prosperity. This indirectly conveys that selfishness is a quality that is to be discarded while seeking emancipation. The Self within is always the same in all the beings, reveals Upaniṣad-s. Similarly, giriśanta also refers to the essence of Vedas, viz. Upaniṣad-s. Therefore, giriśanta means Lord of knowledge (for emancipation).