It is a classical problem to study incidences between a nite number of points and a nite number of geometric objects. In this presentation, we see that continuous incidence theory can be used to derive a number of results in geometry, geometric measure theory, and analytic number theory. The applications to geometry include a fractal variant of the regular value theorem. The applications to geometric measure theory include a generalization of Falconer distance problem in which we prove that a compact subset of Rd of sufficiently large Hausdorff dimension determines a positive proportion of all (k+1)-configurations described by certain restrictions. More specifically we consider the set {(x, x1,...,xk)∈Ek+1:||x - xi||B = ti;1≤i≤k}, where B is any convex centrally symmetric body with a smooth bound- ary and non-vanishing curvature. The applications to Number Theory include counting integer lat- tice points in the neighborhood of variable coecient families of sur- faces.