connections between several compact spaces are studied in this thesis. proofs are given when one implies another, and so are counterexamples when one does not. the spaces discussed in this thesis are: uniform eberlein - compact (uec) space, eberlein - compact (ec) space, talagrand - compact (tc) space, gul'ko - compact (gc) space, corson - compact (cc) space, radon-nikody'm - compact (rn) space, rosenthal - compact (rc), valdivia - compact (vc) space. the main results are: (see document)