The primary and the the most authoritative commentary on the yoga sutras is written by a scholar named Vyāsa, not to be confused with Krishna Dwaipayana or Veda Vyāsa, who compiled the Vedas and wrote the Mahābhāratha. It is also known as the Vyāsa Bhāshya.
All major classical sub-commentaries are based on explaining Vyāsa's Bhāṣya, not just Patañjali's Sūtras directly. Thus the Yoga Sutras are always studied with the commentary.
Some other direct commentaries are shown below but Vyāsa's commentary is considered the de-facto standard.
The following are some of the popular sub-commentaries on the Vyāsa Bhāshya. Of these Vāchaspati Mishra's is considered the gold standard sub-commentary on the Vyāsa Bhāshya.
Vācaspati Miśra was an incredibly influential and prolific Indian philosopher and scholar. He is considered a towering figure in Indian philosophy for his expert sub-commentaries on all 6 darshanas of the Indian philosophical system . He is also known as "Sarva-tantra-svatantra". The title "Sarva-tantra-svatantra" (सर्वतन्त्रस्वतन्त्र) is one of the most prestigious and rare honorifics in the history of Indian philosophy. It literally translates to "One who is a sovereign master of all systems."
Swami Hariharananda Aranya's text is chosen due to its traditional structure, precision and clarity. Swami Hariharananda Aranya was also a practicing Yogi and a Sāmkhya scholar. Sāmkhya is the foundation for Yoga since Yoga is the practical wing of Sāmkhya. The English translation, which is the one we normally study, by P.N. Mukherji, is also very good and easy to read. Swamiji also references Vāchaspati Mishra's sub-commentary. For all the aforementioned reasons, this text was chosen for this study.
In the author's opinion, though there are numerous contemporary texts written by modern day authors in the last 40 years on the Yoga Sutras, owing to the popularity of Yoga worldwide due to the association of yoga with asanas, they have one or more of the following defects:
1) Incorrect interpretation that is not based on traditional interpretation (see below for why a traditional interpretation is important)
2) Lacking "to-the-point" explanation of concepts and verbose material that serves no purpose
There is a saying that one should flee from a self taught teacher of the scriptures. Shankaracharya famously said in his Bhagavad Gita Bhashyam "One who is not versed in the traditional lineage (sampradāya), even if he is a knower of all the scriptures, is to be disregarded just like a fool". The scriptures (Śruti) use language that is subtle, often contradictory on the surface, and highly symbolic. Therefore, they can be prone to misinterpretation. For this reason, Sampradāya (Lineage) is the Key to understanding the scriptures. Some modern day authors, translate the Yoga Sutras from Sanskrit to English using the dictionary and this is perhaps the worst way to interpret the Sutras because of the nature of Sanskrit which is highly contextual. The Sanskrit word "aja" (अज) can mean both an unborn and a goat. Therefore which meaning is used is highly contextual.