Ānāpāna-sati: Awareness or mindfulness on & by in-and-out-breathing, is one of the most important trainings for reaching mental concentration and the 4 absorptions jhāna. In the Satipatthāna Sutta M. 10, D. 22 and elsewhere, 4 methods of practice are given, which may also serve as basis for insight meditation. The speech on Awareness by Breathing' Ānāpānasati Sutta, M. 118 and other texts have 16 methods of practice, which divide into 4 groups of four. The first three apply to both calm samatha and insight-meditation, while the fourth refers to pure insight praxis only. With attentive mind he breathes in, with attentive mind he breathes out.
Maha Thera Nyanatiloka. Manual of Buddhist Terms and Doctrines, Buddhist Publication Society, first edition 1952.