  We investigate some of the motivations and consequences of the conjecture
that the Kac-Moody algebra E11 is the symmetry algebra of M-theory, and we
develop methods to aid the further investigation of this idea. The definitions
required to work with abstract root systems of Lie algebras are given in review
leading up to the definition of a Kac-Moody algebra. The motivations for the
E11 conjecture are presented and the nonlinear realisation of gravity relevant
to the conjecture is described. We give a beginner's guide to producing the
algebras of E11, relevant to M-theory, and K27, relevant to the bosonic string
theory, along with their l1 representations are constructed. Reference tables
of low level roots are produced for both the adjoint and l1 representations of
these algebras. In addition a particular group element, having a generic form
for all G+++ algebras, is shown to encode all the half-BPS brane solutions of
the maximally oxidised supergravities. Special analysis is given to the role of
space-time signature in the context of this group element and subsequent to
this analysis spacelike brane solutions are derived from the same solution
generating group element. Finally the appearance of U-duality charge multiplets
from E11 is reviewed. General formulae for finding the content of arbitrary
brane charge multiplets are given and the content of the particle and string
multiplets in dimensions 4,5,6,7 and 8 is shown to be contained in the l1
representation of E11.
