Stochastic calculus and stochastic differential equations play an assertive role in many applications including physics, biology, financial and actuarial modelling. Well known phenomena have been described in the past by deterministic differential equations. Due to the presence of indeterminate factors, the same phenomena can be better modelled by stochastic equations. Therefore, stochastic differential equations are more realistic to the real world than the deterministic ones. This book examines new results from different fields of interest in the wide area of stochastic differential equations and their applications.