 Hello my name is Ronnie Sebastian and I'm a faculty at IIT Bombay and in the semester July 2023 I will be offering a course on NPTEL called Points at Topology. This is primarily a course for which most mathematics students see in their master's program, but some glimpses of it you may also see if you have if you are from a strong undergraduate program. So now I want to briefly describe some of the things which we are going to do in this course. So we will begin this course by seeing the definition of a topological space and we will see various tools which allow us to construct new topological spaces from old ones. So this will provide us with lots of examples of topological spaces and we can test our theory on it. That's the first part of the course. In the second part of the course just the way in group theory one of the things we do is define group homophisms that allows us to see how groups they are related to each other which in turn allows us to say more about one particular group. So in the same way we can study one topological space by seeing how it interacts with other topological spaces and these interactions are the notion of a continuous map. So we will define continuous maps between different topological spaces and we will see various properties of continuous maps. In the third part of this course, so we will talk about metric spaces and how a metric space gives rise and how a metric on a set X gives rise to a topology. Metric spaces are a very important class of topological spaces and in some sense our intuition and topology is comes from metric spaces. So we will see some more intuitive descriptions of the concepts we have learned in case of metric spaces, in the special case of metric spaces. Once we have done this, we will introduce topological properties like connectedness and compactness An important collection of topological spaces that we will see would be the vector spaces Rn, GLNR, the general linear group, SNR, the special linear group, orthogonal matrices, special orthogonal matrices, unitary matrices, special unitary matrices and we can ask for all these examples, you know, are they are these topological spaces connected, are they path connected, are they compact, so we will try to answer these questions. So that would be quite interesting. One of the interesting results we will prove in this course is that the group SON is connected, so that would be quite nice. After that we will talk a little bit about locally compact topological spaces and one point compactifications. Then we will introduce the quotient topology, which is very important. The quotient topology allows us to construct more examples of topological spaces. So using the quotient topology, we will construct the grass manians and the projective spaces and once again for these we can ask are these connected, are these compact, are these path connected? And finally, in the last part of this course, we will see what conditions on a topological space will ensure that the topology comes from a metric. So as I had mentioned before, metric spaces are a very important class of topological space and so it's very natural to, it's a very natural question to ask, like what topological spaces are actually metric spaces. The focus of this course is going to be on how to use the results that we have learned as tools to study the various examples of topological spaces, the various important examples of topological spaces that we see throughout this course. Thank you.