The set of almost characters of a finite reductive group whose theory is proposed by Lusztig forms an orthonormal basis of the space of class functions.

It is believed that the almost characters are more theoretically computable than the usual basis of irreducible characters.

In this talk, I would like to give an introduction on the almost characters of a symplectic group or an orthogonal group.

Then I will discuss the decomposition of the Weil character of the dual pair or with respect to the almost characters.