All theoretical and observational topics relevant to the understanding of the thermonuclear (Type Ia) supernova phenomenon are reviewed in this study by a panel including the foremost experts in the field. The book covers all aspects, ranging from the observations of SNe Ia at all stages and all wavelengths to the 2D and 3D modelling of thermonuclear flames in very dense plasmas. Scenarios for close binary evolution leading to SNe Ia are discussed. Particular emphasis is placed on the homogeneity vs. diversity of SNe Ia and on their use as standard candles to measure cosmological parameters. The book reflects the recent and very significant progress made in both the modelling of the explosions and in the observational field.