Hinduism
Hinduism is not so much a religion as a label covering the religious beliefs of the people of India (but not those that already have a name, such as Buddhism, Islam, Christianity, etc.).
The main Hindu idea is that everything is connected. The ultimate reality is brahman.
The world appears multiform but in fact is one. The apparent variety/diversity is called maya, and some Hindus regard it as an illusion.
The self (atman) is part of the whole of reality not a truly separate entity. The self we perceive (including the ego, the body, and the personality) is a result of one's particular environment and upbringing. This is called ahamkara. The true self (i.e. atman) is what thinks, knows, and perceives. This self is not itself known or perceived.
The deepest truth of Hinduism (according to Hindus) is that atman is brahman. Thus the soul is immortal. At death the truly enlightened pass out of this world completely. The rest of us are slaves to our desires, which are shallow and ignorant. We get reincarnated.
Real freedom comes from knowledge of brahman. This requires learning, but also meditation on the atman, withdrawal from ordinary life, and becoming like a child.
A Kantian/Shopenhaurian re-reading of Hinduism:
Brahman : noumenal reality
Maya : phenomenal reality
Ahamkara : phenomenal self
Atman : noumenal self