This paper gives an introduction to the formulation of parametrized va
riational principles (PVPs) in mechanics. This is complemented by more
advanced material describing selected recent developments in hybrid a
nd nonlinear variational principles. A PVP is a variational principle
containing free parameters that have no effect on the Euler-Lagrange e
quations and natural boundary conditions. The theory of single-field P
VPs, based on gauge functions, is a subset of the Inverse Problem of V
ariational Calculus that has limited value. On the other hand, multifi
eld PVPs are more interesting from both theoretical and practical stan
dpoints. The two-dimensional Poisson equation is used to present, in a
tutorial fashion, the formulation of parametrized mixed functionals.
This treatment is then extended to internal interfaces, which are usef
ul in treatment of discontinuities, subdomain linkage and construction
of parametrized hybrid functionals. This is followed by a similar but
more compact treatment of three-dimensional classical elasticity, and
a parametrization of nonlinear hyperelasticity.