11.3 billion years ago a star exploded. It is framed by the constellation Ursa Major. It was photographed in 1997 and it's impact on cosmology theory is still being felt.This exploding star is the Supernova 1997ff type Ia. The discovery and analysis of the radiation that emanates from SN 1997ff is providing support for the theory of "The Accelerating Expansion of our Universe," "Dark Matter," and "Dark Energy".The Hubble discovery also reveals that the universe only recently began speeding up, a discovery that suggests the universe is expanding more quickly than in the past, but there were alternate explanations. The accelerating expansion of the universe is the observation that the universe appears to be expanding at an increasing rate, so that the velocity at which a distant galaxy is receding from the observer is continuously increasing with time.The accelerated expansion was discovered in 1998, by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which both used distant type Ia supernovae as standard candles to measure the acceleration.The expansion of the universe is thought to have been accelerating since the universe entered its dark-energy-dominated era roughly 5 billion years ago. Within the framework of general relativity, an accelerating expansion can be accounted for by a positive value of the cosmological constant (Lambda), equivalent to the presence of a positive vacuum energy, dubbed "dark energy". While there are alternative possible explanations, the description assuming dark energy (positive Lambda) is used in the current standard model of cosmology, which also includes cold dark matter (CDM) and is known as the Lambda-CDM model.This book focuses on our Accelerating universe and the theories that support it.This book is designed to be a state of the art, superb academic reference work and provide an overview of the topic and give the reader a structured knowledge to familiarize yourself with the topic at the most affordable price possible.The accuracy and knowledge is of an international viewpoint as the edited articles represent the inputs of many knowledgeable individuals and some of the most current knowledge on the topic, based on the date of publication.