### 1. INTRODUCTION

This review discusses several aspects of the cosmological constant both
from the cosmological and field theoretical
perspectives with the emphasis on conceptual and fundamental
issues rather than on observational details.
The plan of the review is as follows: This section introduces the key
issues related to
cosmological constant and provides a brief historical overview.
(For previous reviews of this subject, from cosmological point of view,
see [1,
2,
3,
138].)
Section 2 summarizes the kinematics and dynamics
of the standard Friedmann model of the universe
paying special attention to features involving the cosmological
constant. Section 3
reviews the observational evidence for cosmological constant, especially
the supernova results, constraints from the age of the universe and a
few others. We next study models with evolving
cosmological `constant' from different perspectives.
(In this review, we shall use the term
cosmological constant in a generalized sense including the scenarios in
which cosmological "constant"
is actually varying in time.) A phenomenological parameterization is
introduced in section 4.1 to compare theory
with observation and is followed
up with explicit models involving scalar fields in
section 4.2. The emphasis
is on quintessence and tachyonic scalar field models and the cosmic
degeneracies introduced by them. Section 5
discusses cosmological constant
and dark energy in the context of models for structure formation and
section 6
describes the constraints arising from CMBR anisotropies.

The latter part of the review
concentrates on more conceptual and fundamental aspects of the
cosmological constant. (For previous reviews of this subject, from a
theoretical physics perspective,
see [4,
5,
6].)
Section 7 provides
some alternative interpretations of the cosmological constant which
might have a bearing on the possible solution to the
problem. Several relaxation mechanisms have been suggested in the
literature to reduce
the cosmological constant to the currently observed value and some of these
attempts are described in Section 8.
Section 9 gives a brief description of
the geometrical structure of the de Sitter spacetime and the
thermodynamics of the de Sitter universe is taken up in
section 10. The relation between horizons,
temperature and entropy are presented at one go in this section and the
last section deals with the role of string theory in the cosmological
constant problem.