  In this work we investigate connections between superalgebras and their
realizations in terms of particles, branes and field theory models. We start
from Poincar\'e superalgebras with brane charges and study its representations.
The existence of new supermultiplets in different dimensions including an ultra
short supermultiplet in D=11 different from the supergravity multiplet is
shown. Generalizations of superalgebras containing brane charges, including
those in D$>$11 are considered. The realization of these algebras at the level
of relativistic particle models and, upon quantization, at the level of field
theory is presented. Application of Hamiltonian/BRST methods of quantization of
systems with mixture of first and second class constraints as well as a
conversion method are discussed for the models of interest. Using quantization
of particle mechanics we obtain information on the spectrum and linearized
equations of motion of the perturbative, linearized M-theory. The
generalization of particle models to p-branes is made using a geometrical
formulation of superembedding approach to study the example of L-branes which
have a linear multiplet on their worldvolume. The p-branes and strings in
B-field are considered as well as the origin of noncommutativity and
non-associativity in their low-energy limit. It is shown that the application
of Hamiltonian/BRST methods for those models leads to stringy version of
Seiberg-Witten map and the removal of the non-associativity/noncommutativity.
