How about we approach it this way. Rather than a free-for-all of every Hindu here just tossing beliefs or philosophies into the pot, let's start with these from Core Beliefs of Hindus - dummies and add/subtract from there:
Truth is eternal.
Hindus pursue knowledge and understanding of the Truth: the very essence of the universe and the only Reality. According to the Vedas, Truth is One, but the wise express it in a variety of ways.
Brahman is Truth and Reality.
Hindus believe in Brahman as the one true God who is formless, limitless, all-inclusive, and eternal. Brahman is not an abstract concept; it is a real entity that encompasses everything (seen and unseen) in the universe.
The Vedas are the ultimate authority.
The Vedas are Hindu scriptures that contain revelations received by ancient saints and sages. Hindus believe that the Vedas are without beginning and without end; when everything else in the universe is destroyed (at the end of a cycle of time), the Vedas remain.
Everyone should strive to achieve dharma.
Understanding the concept of dharma helps you understand the Hindu faith. Unfortunately, no single English word adequately covers its meaning. Dharma can be described as right conduct, righteousness, moral law, and duty. Anyone who makes dharma central to one’s life strives to do the right thing, according to one’s duty and abilities, at all times.
Individual souls are immortal.
A Hindu believes that the individual soul (atman) is neither created nor destroyed; it has been, it is, and it will be. Actions of the soul while residing in a body require that it reap the consequences of those actions in the next life — the same soul in a different body.
The process of movement of the atman from one body to another is known as transmigration. The kind of body the soul inhabits next is determined by karma (actions accumulated in previous lives). Learn more about Hindu funeral customs.
The goal of the individual soul is moksha.
Moksha is liberation: the soul’s release from the cycle of death and rebirth. It occurs when the soul unites with Brahman by realizing its true nature. Several paths can lead to this realization and unity: the path of duty, the path of knowledge, and the path of devotion (unconditional surrender to God).