  We carry out a detailed Lie point symmetry group classification of the
Li\'enard type equation, $\ddot{x}+f(x)\dot{x}+g(x) = 0$, where $f(x)$ and
$g(x)$ are arbitrary smooth functions of $x$. We divide our analysis into two
parts. In the present first part we isolate equations that admit lesser
parameter Lie point symmetries, namely, one, two and three parameter
symmetries, and in the second part we identify equations that admit maximal
(eight) parameter Lie-point symmetries. In the former case the invariant
equations form a family of integrable equations and in the latter case they
form a class of linearizable equations (under point transformations). Further,
we prove the integrability of all of the equations obtained in the present
paper through equivalence transformations either by providing the general
solution or by constructing time independent Hamiltonians. Several of these
equations are being identified for the first time from the group theoretical
analysis.
