This eBook entitled "Reliability Theory and its Applications" is primarily devoted to papers from the 2nd International Conference on Mathematical Techniques in Engineering Applications (ICMTEA2016), which was successfully held at the Graphic Era University, Dehradun on 29-30 April, 2016.The conference had 11 invited speakers from the expert of advances in mathematics and engineering areas. The invited speakers gave an in-depth understanding of their field of expertise. There were discussions on stimulations in simple dynamical systems, the mathematical perspective of control theory. The discussions also included the role of regression-based approach in software reliability engineering, cascading failure models and system reliability, risk-informed modelling and decisions for complex engineering systems. There were interesting talks on ecology to energy through mathematical models: sustainable biodiesel production, soft computing approaches in technical diagnostics. The speakers also discussed the optimal joint harvest of a prawn fishery and a poultry of birds in a linked bioeconomic system, designing near-optimal irregular experimental plans satisfying multi-optimality criteria etc. There was a talk about a major breakthrough in the dynamics of the logistic map.