A topos is a Cartesian closed category with all finite limits and a subobject classifier. In his two seminar talks (of which this is the first) James Clift will explain all of these terms in detail. In this talk he defines products, pullbacks, general limits, and exponentials and in Part 2 he will explain subobject classifiers.
The lecture notes are available here: therisingsea.org/notes/ch2018-lecture4.pdf.
For the general seminar webpage see therisingsea.org/post/seminar-ch/.