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Ashtanga Yoga( Eight limbs of Yoga) : Mahrishi patanjali has mentioned about Ashtanga Yoga in patanjali yoga sutra. In sadhanpada he has explained about eight limbs of yoga and he has explained nicely like everyone can practice these eight limbs{yama(Social discipline), niyama(self discipline), Asana( posture), pranayama, pratyahara, Dharana, Dhyana, Samadhi} and can achieve enlightenment .

he has explained like firstly you should behave nicely and in a discipline way in society than you should follow  self discipline after this you can practice asanas, pranayamas, Dharna , Dhyana, Samadhi. These are like a ladder you have to follow step by step to reah your ultimate goal slowly.

In hatha Yoga Swami swatmarama has mentioned like u don't need to follow first two yamas and niymas straight way you can start your practice of Asana, pranayamas, Kriyas and Nada anusandhana.

both are having same goal at last to achieve enlightenment .

Ashtanga yoga is more helpful and easy to practice 

Modern ashtanga Yoga: In this you have three series. primary series , secondary series and third series. 

Firstly you practice primary series once you are master in all asanas than you perform secondary series. Smae way once you become master of secondary series than you practice third seuance. It improves your stemina  and tone up your muscles.

Nada Anusandhana is a practice of hatha yoga which leads to samadha the ultimate goal of Yoga. In 4th Chapter of Hathayogapradipika swami swatmaram has clearly mentioned about Nada Anusandhana. Once you get Master of asanas kriyas, pranayamas through hatha yoga practices then automatically a sound starts inside your body than you have to sit silently and listen this sound. Slowly gradually it starts to makes different differnt kinds of nada that is only Nada anusandhana which leads to samadhi the ultimate goal of Yoga .

Hatha yoga is best of all yogic practices as in this you are not focusing only on physical body. you are completely aware of of physical and mental piece. during this practice you are making balance between Ha and tha nadis which is your left and right nostril. During hatha yoga practice u sometimes you force with the body but you always enjoy your deeperness and mentle piece. during hatha yoga practice you get a great satisfaction and  deep realxation.

During posture you get more strength, flexibility and it improves your co-ordination at the same time mental relaxation. during kriyas and pranayama you get inner cleanliness.