First of all let me say that this is a huge subject, of which I have only just scratched the surface. It would be possible to spend years studying Judaism, it has many subtleties and complexes that my brief study will have missed.
At first glance the key concept of the unity of God may appear as a direct opposite to the Hindu idea of one God with many manifestations. If we look at the Zohar, a collection of works on Kabbbalah (Jewish Mysticism) we can see that there is a concept of different aspects of God in the Jewish tree of life.
This tree is made up of Sephiroth or aspects of God. The idea is that God can manifest in different ways. These have descriptions such as Binah, represtenting Understanding/ repentance/ reason, but also associated with “the higher mother”. Similarly relationships such as “bride” and “son” are represented in the tree of life. David R. Blumenthal, Professor of Judaic Studies, Emory University, Georgia, USA writes:
The historical interlude of the Christian reception of the Zohar in counterreformation Italy aside, it seems to me that a more profound theological question has arisen: If God can, indeed, have personalist dimensions as part of God’s own inner being, why should there be only three such dimensions? If God can, indeed, encompass different levels of being, all of which are equal within God’s inner-ness, why should there not be as many such levels as necessary? To put it clearly: If God’s being is plural, why only Father, Son, and Holy Spirit? Why not Ineffability, Knowability (Father), Intuition (Mother), Grace (male), Judgment (female), Compassion (Husband), Eternity, Awe, Fecundity (male), and Providence (Bride, Mother) — all of which are equally integral to the divine whole? To put it in declarative form: The zoharic dialogue with the trinity leads to the statement: Three is not enough! God, in God’s fullness, is more than three. God, in Whose Image humanity is created, has more than three dimensions. The awesome complexity of the human personality — in which Image humanity is created — suggests that there are many more than three basic dimensions to God’s personhood. Indeed, if we, humans, are more than trinitarian, certainly God is more than three. (From Three is not enough).
This view certainly coincides with very closely with Hindu views of God. I think that the Judaic tree of life is described in abstract terms because of the biblical dictates against making images of God. This prevented Jewish mystics from using straightforward images as Hindus do.
This aspect of the Kabbalha corresponds closely with the Hindu Jnana Yoga. Judaism also has equivalent ideas to Bhakti Yoga. The founder of Hassidic Judaism Baal Shem Tov saw prayer and devotion as more important than the study of the Talmund and the tree of life. He also saw great importance on purity. He declared the whole universe, mind and matter, to be a manifestation of the Divine Being; that this manifestation is not an emanation from God, as is the conception of the Kabbalah by Mitnagdim, for nothing can be separated from God, echoing Advaita Vedanta.
There have also been attempts to show that the tree of life reflect the Yogic chakras. Altogether, there are striking parallels between Judaism and Hinduism. Some of these certainly emerged as mystical revelation. It is also possible that some of these concepts were within Judaism from the beginning, echoing the original true world religion.