The Śrī Guru Gītā is very popular in India. It originated in Mahārāṣṭra, we don’t know exactly when.
It is a dialogue between Śiva and Śakti, between Īśvara and Pārvatī. It is said to come from the Skandapurāṇa – this is a traditional Hindu text attribution, to give the text credibility when the origin is not known.
Some scholars have claimed that the text comes from the Śrī Guru Caritra. In reality it was added in at a later stage, only around the 18th century. The academic who established this is Antonio Rigopoulos and his Guru Gītā essay can be found in Theory & Practice of Yoga. We have independent manuscripts of the Guru Gītā and of the Śrī Guru Caritra without the Guru Gītā in it.
The most popular existing translation was done by Swami Prajñānanda, whose Sanskrit was good but who often did not understand the scriptural background of the verses she was translating, and in these cases she was unable to convey the meaning of the verse correctly. Though she did translate the majority of verses more or less correctly, we can often understand a given verse much more deeply by looking at the different ways it could be translated. Needless to say, you need the help of a Sanskrit scholar to do this.
Please watch this video in which Hareesh gives an explanation of the Guru-dhyāna verse that precedes the beginning of the text proper (Haṁsābhyāṁ parivṛtta-patra-kamalair…):
Hareesh’s translation of three important verses of the text:
Gurur buddhyātmano nānyat satyaṁ satyaṁ na saṁśayaḥ |
Tallābhārthaṁ prayatnas tu kartavyo hi manīṣibhiḥ ||9||
“The Guru is none other than the discerning self. Without a doubt, this is the truth. So prudent individuals should make an effort to attain that [discernment, i.e. the inner Guru].”
Gūḍhavidyā jaganmāyā dehe cājñāna-sambhavā |
Udayaḥ yatprakāśena guru-śabdena kathyate ||10||
“In the body there lives both hidden wisdom and powerful delusion born of ignorance. The one whose illuminating teaching causes [the hidden wisdom] to surge up within is designated by the word guru.”
The hidden wisdom (gūḍhavidyā) of verse 10 and the inner Guru (buddhyātman) of verse 9 are one and the same.
Haṁsābhyāṁ parivṛtta-patra-kamalair divyair jagat-kāraṇair
viśvotkīrṇam aneka-deha-nilayaiḥ svacchandam ātmecchayā |
Tad-dyotaṁ pada-śāmbhavaṁ tu caraṇaṁ dīpāṅkura-grāhiṇaṁ
pratyakṣākṣara-vigrahaṁ guru-padaṁ dhyāyed vibhuṁ śāśvatam ||
“One should meditate on the eternal all-pervasive state of the Guru, which is the embodiment of all the sacred sounds [of Sanskrit] in visible form. One should meditate on the [form of] practice & conduct which holds ‘the flame of the lamp’, that is, the Śāmbhava state which illumines that spontaneous freedom (svacchanda) which is inscribed in everything in existence by the divine Causes of the World that have all bodies as their abode, and which are [installed within] the ‘lotuses’ (i.e. chakras) whose petals are rotated by ‘ham’ and saḥ’.”