  This thesis deals with the enumerative study of combinatorial maps, and its
application to the enumeration of other combinatorial objects.
  Combinatorial maps, or simply maps, form a rich combinatorial model. They
have an intuitive and geometric definition, but are also related to some deep
algebraic structures. For instance, a special type of maps called
constellations provides a unifying framework for some enumeration problems
concerning factorizations in the symmetric group. Standing on a position where
many domains meet, maps can be studied using a large variety of methods, and
their enumeration can also help us count other combinatorial objects. This
thesis is a sampling from the rich results and connections in the enumeration
of maps.
  This thesis is structured into four major parts. The first part, including
Chapter 1 and 2, consist of an introduction to the enumerative study of maps.
The second part, Chapter 3 and 4, contains my work in the enumeration of
constellations, which are a special type of maps that can serve as a unifying
model of some factorizations of the identity in the symmetric group. The third
part, composed by Chapter 5 and 6, shows my research on the enumerative link
from maps to other combinatorial objects, such as generalizations of the Tamari
lattice and random graphs embeddable onto surfaces. The last part is the
closing chapter, in which the thesis concludes with some perspectives and
future directions in the enumerative study of maps.
