  A 1-bridge torus knot in a 3-manifold of genus $\le 1$ is a knot drawn on a
Heegaard torus with one bridge. We give two types of normal forms to
parameterize the family of 1-bridge torus knots that are similar to the
Schubert's normal form and the Conway's normal form for 2-bridge knots. For a
given Schubert's normal form we give algorithms to determine the number of
components and to compute the fundamental group of the complement when the
normal form determines a knot. We also give a description of the double
branched cover of an ambient 3-manifold branched along a 1-bridge torus knot by
using its Conway's normal form and obtain an explicit formula for the first
homology of the double cover.
