: In this thesis, we present an expanded account of Optimal Incomplete Block Designs based on an article by J.P. Morgan (2007). In this thesis optimal incomplete block designs are pursued through the E-criterion of minimizing maximal variance. Methodology is developed for design choice based on. Along with the general methodology, a near complete solution for E-optimal block designs is provided for up to 15 treatments. E-optimality is revealed as a flexible criterion that, depending on the application, can offer many choices for good designs. In last chapter we study optimal incomplete block designs when there are two blocks and their sizes are equal. It turns out that a binary design of a certain pattern is A- and D-optimal in the 5 v= 6 both the binary design and the non-binary design are E-optimal.