  This review paper is a continuation of hep-th/0012145 and it deals primarily
with noncommutative ${\mathbb R}^{d}$ spaces. We start with a discussion of
various algebras of smooth functions on noncommutative ${\mathbb R}^{d}$ that
have different asymptotic behavior at infinity. We pay particular attention to
the differences arising when working with nonunital algebras and the unitized
ones obtained by adjoining the unit element. After introducing main objects of
noncommutative geometry over those algebras such as inner products, modules,
connections, etc., we continue with a study of soliton and instanton solutions
in field theories defined on these spaces. The discussion of solitons includes
the basic facts regarding the exact soliton solutions in the Yang-Mills-Higgs
systems as well as an elementary discussion of approximate solitons in scalar
theories in the $\theta \to \infty$ limit. We concentrate on the module
structure and topological numbers characterizing the solitons. The section on
instantons contains a thorough description of noncommutative ADHM construction,
a discussion of gauge triviality conditions at infinity and the structure of a
module underlying the ADHM instanton solution. Although some familiarity with
general ideas of noncommutative geometry reviewed in the first part is expected
from the reader, this part is largely independent from the first one.
