The Nyāya Sūtras is an ancient Indian Sanskrit text composed by Akṣapāda Gautama, also known as Aksapāda, and is the foundational text of the pracina or Old Nyaya school of Hindu philosophy.
The text contains 5 parts divided further into chapter and contains over 500 sutras.
Babaji is reading from Nyāya-darśanam with the Vātsyāyana's bhāsya, which includes the Hindi commentary by Dhundhiraj Shastri.
You have to have a clear definition of your goal – what do I want? What am I heading for? You have to have a very clear definition of what is Bhakti. If you are not clear, then you can remain in a hazy field for a long time. That is the significance of Nyaya. It gives clear definitions, which is very important. Otherwise you may think that this is the definition of Bhakti and I am doing Bhakti, but what you may be doing may not fit the definition.