This thesis is concerned with heat kernel estimates on weighted Dirichlet spaces. The Dirichlet forms considered here are strongly local and regular. They are defined on a complete locally compact separable metric space. The associated heat equation is similar to that of local divergence form differential operators. The weight functions studied have the form of a function of the distance from a closed set [SIGMA], that is, x [RIGHTWARDS ARROW] a(d( x, [SIGMA])). We place conditions on the geometry of the set [SIGMA] and the growth rate of function a itself. The function a can either blow up at 0 or [INFINITY] or both. Some results include the case where [SIGMA] separates the whole spaces. It can also apply to the case where [SIGMA] do not separate the space, for example, a domain Ω and its boundary [SIGMA] = ∂Ω. The condition on [SIGMA] is rather mild and do not assume differentiability condition.