Jiva translates from Sanskrit as individual soul, and Mukti means liberation. Jivamukti yoga was founded by Sharon Gannon and David Life in 1984 in New York City. It was (and is by my estimation) the harbinger of what we know as modern vinyasa flow yoga in the west, with reverence to the 5,000-year old spiritual tradition of Yoga. Jivamukti is an integrated practice that honors the physical, philosophical and spiritual branches of yoga. Each class emphasizes the importance of practicing with an elevated intention, breath awareness (breaths are counted), mantra, an uplifting soundtrack, and getting to the heart of yoga, Self-study (swadhyaya) through self-inquiry, which is, I believe, what this whole being alive thing is all about.
Ashtanga yoga is a system of yoga transmitted to the modern world by Sri K. Pattabhi Jois (1915-2009), who learned from his teacher Krishnamacharya, who learned from his teacher, and you know how it goes. This method of yoga involves synchronizing the breath with a progressive series of postures—a process producing intense internal heat and a purifying sweat that detoxifies muscles and organs. The result is improved circulation, a light and strong body, and a calm mind, and ostensibly, samadhi. This method is really smart, and really effective, and requires a lot of dedication. I believe it also has application to those of use who can't practice 6 days a week at 5 am (tho hats off to those who do). Instead I hope to share this rich practice through my own experience and voice as authentically as I can.