The course “Topics in differential  geometry” introduces  basic and important objects which are widely used in mathematics and physics : vector fields and differential  forms. Firstly, we propose a geometric point of view on differential equations using the langage of vector fields, their integral curves and their flows. Secondly, we define differential forms and the exterior differentiation of such forms. Many formulas used in physics (Gauss- Green-Riemann-Ostrogradski-Stokes) are naturally expressed  and unified in those terms and will illustrate the course.