This video introduces the notion of Lie groups, which are basically infinite groups which can be studied using differential geometric methods. We give some basic examples including GL_n and the unitary group U(n) which are important to much of mathematics and physics. We go through the notions of both Lie subgroups and quotient Lie groups via examples. We observe how taking the quotient of a Lie group by a discrete subgroup makes the topology more complicated, and a result which essentially reverses this procedure, namely, that the simply connected cover of a Lie group is itself naturally a Lie group.
