Next Step for Self-Learning

Question

I am an undergraduate mathematics major and recently completed a course in real analysis. While I enjoyed this course it left out many topics that I would have liked to learn because of time constraints. These included Riemann integration, sequences of functions, and series along with their convergence. Along with learning these topics I would like to get a more general idea of the topics we did cover using only the normal Euclidean absolute value metric. The course felt incomplete at times because this is not the only available way to think of distance but just the standard way. These topics include sequences, limits and continuous functions. Would it be recommended to study a subject such as metric spaces or topology in order to get a more abstract view of the topics that were covered in the course? If this is a good course of action should I fill the gaps from the topics that weren't covered before embarking on this or are those topics not so important in metric spaces and topology? Thank you for any answers.