American Swamijis or The Western Yogis
Sister Nivedita
The first Western Hindu who became very well known in India was sister Nivedita. She was a disciple of Swami Vivekananda. All of us know about her. But what is noteworthy is that she was the first Westerner to approve and take to Image worship. Read her book "Kali the Mother".
Sister Nivedita was officially invited to deliver a lecture on “Kali-worship” at the famous Kalighat Temple in Calcutta in 1899. It was a time when not everyone was allowed even to enter the temple. Nivedita was perhaps not the first European to declare herself in Public to be a Hindu at the beginning of the last century, but she was definitely one of the most prominent one.
Though this is not directly related to the topic, you may find these reminiscences of Swami Vivekananda by Sister Nivedita interesting.
http://www.vivekananda.net/PDFBooks/Reminiscences/Nivedita.html
Sir John Woodroffe (Arthur Avalon)
He was a Justice of the High court. Alongside his judicial duties he studied Sanskrit and Hindu philosophy and was especially interested in the Tantric Shakti system. He translated some twenty original Sanskrit texts under his pseudonym Arthur Avalon. He published and lectured prolifically on Indian philosophy and a wide range of Yoga and Tantra topics. His work helped to unleash in the West a deep and wide interest in Tantra, Hindu philosophy and Yogic practices.
Most of us would have read at least one of his books.
Swami Sivananda Radha (Swami Sivananda Radha Saraswati)
She was the first western woman to be initiated into the order of the Dasanami monks. Sister Nivedita did not formally become a Sannyasin. Even today the Ramakrishna order does not initiate women into formal Sannyasa. Swami Sivananda Radha was a disciple of Swami Sivananda. Shortly after the initiation Swami Sivananda sent her back to the West to "update the Teachings for the Western mind."
Upon her return to Canada, she worked unceasingly to fulfill the promise she had made to Sivananda. Her approach to the Hinduism was straightforward, accessible and intensely practical. Her goal was to help people discover the purpose of their lives and to guide them in achieving spiritual and emotional independence.
She thought that her dancing would be given up as part of her renunciation. However, Swami Sivananda had other ideas. He encouraged her to find the sacred in the dance, showing her that the body could be a spiritual tool. Prayer dance became part of her teachings helping students learn how to transform their emotions into devotion through the beautiful gestures of Indian dance.
The science of yoga is the heart of Swami Radha's teaching. Her writings include, Kundalini: Yoga for the West, Mantras: Words of Power, and Hatha Yoga the Hidden Language. These books are popular and distinctive because they clarify the sometimes enigmatic Hindu teachings in a way that can be understood and and applied in western daily life.
Sivaya Subramuniyaswami
Was born in Oakland, California and adopted Saivism as a young man. He travelled to India and Sri Lanka where he received initiation from Sage Yogaswami of Jaffna in 1949. In the 1970s he established a Hindu monastery in Kauai, Hawaii and founded the magazine "Hinduism Today". The author of many books on Hinduism and metaphysics, Subramuniyaswami was one of the most prominent faces of Hinduism during the last two decades of the 20th century.
He was a pioneer and also of great interest to Tamil Brahmins because he was a Shaiva and his teachings are based on Saiva Siddhanta.
Professor Klaus Klostermaier, one of the world's leading specialists on Hindu studies, said in his A Survey of Hinduism:
"Sivaya Subramuniyaswami ... did much to propagate a kind of reformed Saivism through his books. As founder-editor of Hinduism Today, an illustrated monthly, he became the single-most advocate of Hinduism outside India. His Himalayan Academy trains Indian and Western Hindu monks and his Hindu Heritage Endowment provides a source of income especially for priests belonging to the Saiva Siddhanta sampradaya worldwide. Subramuniya was honored and recognized by Hindu leaders in India and broad."
In another aspect he is different from all other teachers. He believed in conversion to Hinduism and his book "How to Become a (Better) Hindu" is a must read for every Hindu.
http://www.himalayanacademy.com/resources/books/hbh/
The entire book is on line free. All his books are available on line free.
He was acclaimed by both Indians and westerners. He was totally accepted by the Indians. If you look at his photograph the only word which comes to your mind "Shivap Pazham".
1986 - New Delhi's World Religious Parliament named him one of five modern-day Jagadacharyas, world teachers, for his international efforts in promoting and chronicling a Hindu renaissance.
1993 - Chicago: at the centenary Parliament of the World's Religions, he was elected one of three presidents, along with Swami Chidananda Saraswati of the Divine Life Society and Mata Amritanandamayi, to represent Hinduism at the Presidents' assembly, a core group of 25 men and women voicing the needs of world faiths.
1995 - Delhi, the World Religious Parliament bestowed on him the title Dharmachakra for his remarkable publications.
1998 - The Vishva Hindu Parishad of Kerala sent an envoy to Kauai to honor and recognize him as the "Hindu Voice of the Century."
You can read the magazine "Hinduism today" here. The subscription is free.
http://www.hinduismtoday.com/
Sri Daya Mata
The current president and Sanghamata (Mother of the Society) of the Self-Realization Fellowship (SRF Inc.) Los Angeles and the Yogoda Satsanga (YSS Inc.) Society in India.
She written three books: Only Love': Living the Spiritual Life in a Changing World, Finding the Joy Within You: Personal Counsel for God Centered Living, and Enter the Quiet Heart: Creating a Loving Relationship with God.
Swami Agehananda Bharati
Originally from Vienna - Professor of Anthropology at Syracuse University for over 30 years. He was a respected academic Sanskritist, a prolific writer on religious subjects, and a monk in the Dasanami Sannyasi order.
His book "The Tantric tradition" is considered a classic on Tantra.
Swami Satyananda Saraswati
Author of Chandi Path, Kali Puja and many other books on Hinduism. A Dasanami Monk. He has an ashram in California. Unlike the other teachers he emphasizes ritualistic Hinduism especially Yagnas.
Most of his books are not available in India. Meant exclusively for American Hindus.
Ma Jaya Sati Bhagavati - Kashi Ashram
The first American Hindu Godwoman. She teaches from profound personal revelation, in the tradition of her teacher, Swami Nityananda of Ganeshpuri, and her Guru, Neem Karoli Baba.
Babaji Bob Kindler
Spiritual director of the Sarada Ramakrishna Vivekananda Association (SRV) of Oregon, San Francisco, and Hawaii. He is also the founder and Artistic director of Jai Ma Music which offers Sacred Arts events in U.S and other countries.
In addition to composing over 25 albums of devotional and instrumental music, Babaji is an author of many spiritual books. His published titles are:
None of them available in India. Meant exclusively for American Hindus.
Scholars who have helped spread Hinduism
Elizabeth Usha Harding - Author of "Kali, the Black Goddess of Dakshineswar". She has erected a Kali temple in Laguna Beach, California. Dakshineswari Kali.
Please see the virtual temple on the Internet.
http://www.kalimandir.org/Application/Homepage.aspx
Devadutta Kali - Author of "In Praise of the Goddess: The Devimahatmya and Its Meaning".
This is by no means a complete list.