  These Lectures have been given at Laboratori Nazionali di Frascati in the
month of March, 2005. The main idea was to provide our young collegues, who
joined us in our attempts to understand the structure of $N$-extended
supersymmetric one-dimensional systems, with short descriptions of the methods
and techniques we use. This was reflected in the choice of material and in the
style of presentation. We base our treatment mainly on the superfield point of
view. Moreover, we prefer to deal with N=4 and N=8 superfields. At present, the
exists an extensive literature on the components approach to extended
supersymmetric theories in $d=1$ while the manifestly supersymmetric
formulation in terms of properly constrained superfields is much less known.
Nevertheless, we believe that just such formulations are preferable.
  In order to make these Lectures more or less self-consistent, we started from
the simplest examples of one-dimensional supersymmetric theories and paid a lot
of attention to the peculiarities of $d=1$ supersymmetry. From time to time we
presented the calculations in a very detailed way. In other cases we omitted
the details and gave only the final answers. In any case these Lectures cannot
be considered as a textbook in any respect. They can be considered as our
personal point of view on the one-dimensional superfield theories and on the
methods and techniques we believe to be important.
  Especially, all this concerns Section 3, were we discuss the nonlinear
realizations method. We did not present any proofs in this Section. Instead we
focused on the details of calculations.
  Finally, we apologize for the absolutely incomplete list of References.
