  We analyze cosmological perturbations to the linear order in the context of
inflation with an arbitrary number of scalar fields. The fields take values on
a non-trivial manifold with a positive-definite metric and are non-minimally
coupled to Einstein gravity. The perturbations are decomposed into three
different types. The scalar-type perturbations are presented in a gauge-ready
form without fixing the temporal gauge condition, as well as in terms of
gauge-invariant variables. The gauge-ready method enables us to impose
different gauge conditions which are most suitable to the problem at hand. We
quantize the scalar perturbations and obtain the solutions.
