Complemented and uncomplemented subspaces of Banach spaces

"A natural process in examining properties of Banach spaces is to see if a Banach space can be decomposed into simpler Banach spaces; in other words, to see if a Banach space has complemented subspaces. This thesis concentrates on three main aspects of this problem: norm of projections of a Banach space onto its finite dimensional subspaces; a class of Banach spaces, each of which has a large number of infinite dimensional complemented subspaces; and methods of finding Banach spaces which have uncomplemented subspaces, where the subspaces and the quotient spaces are chosen as well-known classical sequence spaces (finding non-trivial twisted sums)." --Abstract.Master of Mathematical Science