Ian Anderson and Iiro Honkala: A Short Course in Combinatorial Designs, ii + 39 pagesin postscript form, click here.
This set of lectures notes has been used for a short, half-semester course, after another half-semester course in combinatorial enumeration. Only a small number of topics are therefore covered and the emphasis is in presenting classical, elegant connections between various combinatorial objects: e.g., how the binary Golay code is defined using a cyclic difference set and produces the Steiner systems S(5,6,12) and S(5,8,24), how the existence of a projective plane of order n is equivalent with the existence of n-1 mutually orthogonal Latin squares of order n, and how Steiner triple systems can be constructed from a Latin square. Many of the results are obtained using elementary linear and abstract algebra.
For a more thorough treatment on design theory, we would like to recommend the book
Ian Anderson: Combinatorial Designs and Tournaments, Oxford University Press, 1997.