This will be the second and final lecture on nuclear spaces. Other topologies on the tensor product, the inductive topology, and the topology of bi-equicontinuous convergence will be defined. Also, topologies on dual spaces such as the weak, Mackey and strong topologies will be introduced. We will see how these topologies simplify in the case of a nuclear Frechet spaces, which will allow us to prove the properties stated at the beginning of the first lecture.