Here are the slides and some references for the courses I am currently teaching.
1. Non-Hausdorff Topology and Domain Theory by Jean Goubault-Larrecq
A very nice introduction to both topology and order theory.
2. Topology and Groupoids by Ronald Brown
Another nice introduction to topology, including (topological) neighbourhood systems.
3. Convergence Foundations of Topology by Frédéric Mynard and Szymon Dolecki
A very interesting approach to topology via convergence.
(Note: the general neighbourhood systems in lecture 1 are the "pretopologies" found here).
4. Continuous Lattices and Domains by G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove and D. S. Scott
The canonical reference for order theory and (locally compact) topology.
5. Frames and Locales: Topology without points by Jorge Picado and Aleš Pultr
An excellent modern reference for point-free topology.
6. Stone spaces by Peter T. Johnstone
The classic reference for point-free topology.
7. Lattice Theory by Garrett Birkhoff
The classic reference for lattice theory.
8. General Lattice Theory by George Grätzer
Another classic reference for lattice theory, including the author's generalisation of Stone's original duality to distributive join-semilattices. The 2nd edition also includes some interesting appendices by various people.
9. Introduction to Lattices and Order by B. A. Davey and H. A. Priestley
Another great lattice theory reference, including Priestley duality.
Introduction to C*-Algebras
1. Lecture Notes on C*-algebras by Ian F. Putnam
Excellent introductory notes on C*-algebras, including groupoid C*-algebras.
2. C*-Algebras and Operator Theory by Gerard J. Murphy.
Probably the best introductory C*-algebra book around.
3. C*-algebras and Their Automorphism Groups by Gert K. Pedersen
My personal favorite but a little tough for the beginner.
4. Operator Algebras: Theory of C*-Algebras and von Neumann Algebras by Bruce Blackadar
A very good encyclopedic up-to-date reference.
5. Hausdorff étale groupoids and their C*-algebras by Aidan Sims
Great introduction to groupoids. The C*-algebra material is more advanced though.
Once we have reviewed the necessary prerequisites, the course will roughly follow Putnam's notes.