In this dissertation, functions in the classes I(p) and I*(p) of close-to-convex and weakly close-to-convex meromorphic functions are discussed.

These functions are analytic in (DELTA)(FDIAG) p with a simple pole at z = p, 0 < p < 1, and normalized by f'(0) = 1. An extension to a larger class J*(p) is also discussed. We say f (ELEM) I(p) if there exists a g (ELEM) (LAMDA)(p), the starlike meromorphic functions with pole at p, and an (VBAR)(alpha)(VBAR) (LESSTHEQ) (pi), (delta) > p such that Re(zf'(z)/e('i(alpha))g(z)) > 0 for (delta) < (VBAR)z(VBAR) < 1.

We say f (ELEM) I*(p) if there exists a g (ELEM) (LAMDA)*(p), the weakly starlike meromorphic functions with pole at p; a P (ELEM) P, the analytic functions of positive real part; and an (VBAR)(alpha)(VBAR) (LESSTHEQ) (pi) so that f'(z) = (e('i(alpha))/(z-p)(1-pz)) g(z)P(z) for (VBAR)z(VBAR) < 1.

For f (ELEM) J*(p) the above statement also holds but f must only be analytic in (DELTA)(FDIAG) z: p (LESSTHEQ) z < 1 with derivative f' which can be analytically extended to (DELTA)(FDIAG) p .

Chapter I discussed basic definitions and conditions for membership in the various classes while Chapters II-IV concern coefficient bounds and integral means about z = 0, z = p, and in the annulus p < (VBAR)z(VBAR) < 1. Lastly, Chapter V discusses the radius of convexity and univalence, and the univalent subclass.