...based on the teachings of Siddhartha Gautama

Quotation:
"Buddhism has the characteristics of what would be expected in a cosmic religion for the future: it transcends a personal God, avoids dogmas and theology; it covers both the natural & spiritual, and it is based on a religious sense aspiring from the experience of all things, natural and spiritual, as a meaningful unity" Albert Einstein

Overview

Buddhism is the fourth largest religion in the world, being exceeded in numbers only by Christianity, Islam and Hinduism. It was founded in Northern India by the Buddha, Siddhartha Gautama. He was born circa 563 BCE in Lumbini which is in modern-day Nepal. At the age of 29, he left his wife, children and political involvements in order to seek truth. It was an accepted practice at the time for some men to leave their family and lead the life of an ascetic. He studied Brahmanism, but ultimately rejected it. In 535 BCE, he attained enlightenment and assumed the title Buddha (one who has awakened).

He is also referred to as the Sakyamuni, (sage of the Sakya clan). He promoted The Middle Way, rejecting both extremes of the mortification of the flesh and of hedonism as paths toward the state of Nirvana. He had many disciples and accumulated a large public following by the time of his death in his early 80's in 483 BCE.

Two and a half centuries later, a council of Buddhist monks collected his teachings and the oral traditions of the faith into written form, called the Tripitaka. This included a very large collection of commentaries and traditions; most are called Sutras (discourses).

As Buddhism expanded across Asia, it evolved into two main forms, which evolved largely independently from each other:

Theravada Buddhism (sometimes called Southern Buddhism; occasionally spelled Therevada) "has been the dominant school of Buddhism in most of Southeast Asia since the thirteenth century, with the establishment of the monarchies in Thailand, Burma, Cambodia and Laos." 
Mahayana Buddhism (sometimes called Northern Buddhism) is largely found in China, Japan, Korea, Tibet and Mongolia. 

To which might be added:
Tibetan Buddhism, which developed in isolation from Theravada and Mahayana Buddhism because of the isolation of Tibet.

Since the late 19th century:
 Modern Buddhism has emerged as a truly international movement. It started as an attempt to produce a single form of Buddhism, without local accretions, that all Buddhists could embrace.

The Religions Core Beliefs

Buddhism, like most of the great religions of the world, is divided into a number of different traditions. However, most traditions share a common set of fundamental beliefs.

One fundamental belief involves reincarnation: the concept that one must go through many cycles of birth, living, and death. After many such cycles, if a person releases their attachment to desire and the self, they can attain Nirvana  - a state of liberation and freedom from suffering.

The Four Noble Truths

The Buddha's Four Noble Truths explore human suffering. They may be described (somewhat simplistically) as:

1) Dukkha: The reality and universality of suffering. Suffering has many causes: loss, sickness, pain, failure, the impermanence of pleasure.

2) Samudaya: The cause of suffering is a desire to have and control things. It can take many forms: craving of sensual pleasures; the desire for fame; the desire to avoid unpleasant sensations, like fear, anger or jealousy.

3) Nirodha: Suffering ceases with the final liberation of Nirvana (a.k.a. Nibbana). The mind experiences complete freedom, liberation and non-attachment. It lets go of any desire or craving.

4) Magga: The eightfold path leads to the cessation of suffering.

The Five Precepts

These are somewhat analogous to the second half of the Ten Commandments in Judaism and Christianity -- that part of the Decalogue which describes behaviors to avoid.

1. Do not kill
2. Do not steal
3. Do not lie
4. Do not be unchaste
5. Do not consume alcohol or other drugs

The Eightfold Path

The Buddha's Eightfold Path consists of:

Panna: Wisdom: 1) Samma ditthi Right Understanding of the Four Noble Truths
2) Samma sankappa: Right thinking; following the right path in life 
 

Sila: Morality: 3) Samma vaca: Right speech: no lying, criticism, condemning, gossip, harsh language 4) Samma kammanta Right conduct by following the Five Precepts
5) Samma ajiva: Right livelihood; support yourself without harming others 
 
Samadhi: Concentration: 6) Samma vayama Right

Effort: promote good thoughts; conquer evil thoughts
7) Samma sati Right Mindfulness: Become aware of your body, mind and feelings 
8) Samma samadhi Right Concentration: Meditate to achieve a higher state of consciousness.