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Kriya yoga

Tapah svadhyaya ishvara-pranidhana kriya-yogah
Enthusiasm, inquiry and surrender are necessary to thread the path of yoga (The yoga sutras of Patanjali, II-1)

In this first aphorism of the Saddhana Pada, the second chapter of his classic manual on the practice of Raja yoga, Patanjali lists threes of the Niyamas, Tapah, Svadhyaya and Ishvara-pranidhana, stating that practiced together, they constitute Kriya yoga.

Let's first look at each of these:
tapah
The Sanskrit root of the word tapah, tap means to cook, to heat or to burn. Early translators of the sutras, who generally were Sanskrit scholars rather than yoga practitioners, have often translated it as austerities, an unfortunate choice because the word has a negative connotation in Western languages, which Tapah certainly doesn't have in Sanskrit. Alistair Shearers translates it as purification, which is one of its secondary meanings and is undoubtedly a better, if somewhat narrow translation. Matthew Remsky uses endurance, as a way to suggest how Tapah is this quality of determination and discipline needed to deal with the difficulties and set backs which we inevitably meet when we are threading the yoga path. Any translation of Tapah should reflect the fieriness, passion and courage which we need to keep practising, no matter what.
Tapah is akin to viriya (determination), one of the seven factors of awakening in Buddhism.

svadhyaya
The most common translation of the term is (self) study, sometimes even narrowed down to the injunction to study ancient books of wisdom. Alistair Shearers translates it as refinement while Matthew Remsky uses learning. Svadhyaya of course is all of this, as well as this constant, almost childlike curiosity that questions everything. It is akin to dhamma vicaya (investigation of Dhammas), one of the seven factors of awakening in Buddhism. It finds an appropriate expression in the "What is this?" question of Zen Buddhism, or in the "Know thyself" of ancient Greek philosophers. We need it to find our own truth.

ishvara-pranidhana
Because ishvara is usually translated as God (or Supreme Being), the most common translations of ishvara-pranidhana are surrender to God or dedication to God. These translations don't always resonate. with our Western secular culture. Alistair Shearers simply uses surrender, while Godfrey Devereux suggests "absorption in the source" - may be closer to Patanjali's intended meaning.
Unshakeable faith in the guiding and protecting power of the universe is the essence of ishvara pranidhana. In the Kriya yoga context, the soft, feminine quality of ishvara-pranidhana balances the fiery masculine energy of Tapah. Tapah without svadhyaya and ishvara pranidhana just inflates the ego. Ishvara pranidhana helps us recognise that we are not in charge and from there we can cultivate a more trusting relationship with the universe.

According to Zen, the three essential conditions for successful practice are Great Faith, Great Doubt and Great Determination. This accords with this sutra, for without Doubt, why would we inquire, without Determination, how could we succeed in our practice, and without Faith, how could we ever surrender?

The Kriya yoga of Patanjali should not be confused with the yoga system of Mahavatar Babaji and Lahiri Mahasaya, popularised in the West by Paramahansa Yogananda in his book Autobiography of a Yogi.v The Kriya yoga of Patanjali is simply the practice of Tapah, svadhyaya and ishvara-pranidhana. These three preliminary practices aim to neutralise the causes of suffering that are rooted in ignorance and prepare the aspirant for the practice of Aṣṭāṅga (eight limbs) yoga.

Further reading:
The Yoga Sutras Of Patanjali translated by by Alistair Shearer
Threads of Yoga: A Remix of Patanjali’s Sutra’s by Matthew Remski
Yoga Unveiled by Godfrey Devereux