The TM meditation is not exactly free, because in 2002 the TM movement increased the prices for the initiation and switched to a licensing system so that the initiators need sales.
TM meditation is actually just a mantra meditation, to which there are of course many alternatives, both in the form of similar meditations and in the form of other yoga techniques.
Guru Dev Brahmanada Saraswati also taught a Nada-Meditation.
1.1. In principle, everyone can put together a meditation from Sahastra mantras and other common mantras (eg after 'Meditation and Mantras') and possibly always listen to the puja on an MP3 player before the image of the Guru Dev (or one other personally personable gurus) that is easy to find on the Internet.
However, the aspiration should be genuine (introspection, etc.), otherwise it is an abuse - and of course everything at your own risk and then not just stop, not even if it is successful.
Another problem is the neglected effect of a mantra, because even a short bija mantra like AUM is composed of three sounds that have their specific effect. Therefore, mantras have a different effect at every level of consciousness.
The mantra shastra provides some information about this. The mantras of the matrikas serve, for example, to purify certain negative characteristics of the character. The Ashtottara Shatanamavali provides an abundance of mantras, as well as tantric scriptures such as the Todala Tantra. (Tantra means continuum or tissue - everything is connected.)
The mantra initiation with an advanced pundit is of course valuable (VAK).
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A prerequisite for the white path of true Ashtanga yoga is, of course, the practice of Yama und Niyama instead of just using meditation for everyday life, which the Shankara Order also demands, which also follows the eight step path of the Ashtanga-Yoga or the 7 steps of the Yogasutras.