The problem with elementary gender studies courses is the tendency for their instructors to focus on political matters with little consideration given to the philosophy. As Mozibur Ullah stated, to appreciate the philosophical ideas of gender studies it is important to understand how feminism is more than simply a campaign for equal rights, and how gender is more than just a division of bathrooms. It is an epistemological, anthropological, psychological and linguistic assessment of the society in which we live, identifying the patriarchal mould in which society has formed and how it has changed over time.
There are different schools of thought on how philosophy should be taught in general. There are those who like to work from a textbook or two, that broadly and briefly cover the seminal philosophical works and the key ideas; and there are those (like myself) who prefer to avoid such books and get stuck into the juicy heart of the theory from the mouths and pens of the important thinkers themselves.
So depending on how you would prefer to approach this subject, I have different recommendations for you. In both cases, Judith Butler is a significant name. If someone is to be thanked for the subject being called "gender studies" and not simply "feminism" or "women's studies" it is Butler. Her ideas of performed gender and her psychoanalytic and deconstructive seasoning makes her work a joy to read and central to the subject. If you prefer to work from a textbook and get a rough sketch of the whole picture quickly, then I can recommend:
Theorizing Gender (Rachael Alsop, Annette Fitzsimons, Kathleen Lennon)
Judith Butler: Sexual Politics, Social Change and the Power of the Performative (Gill Jagger)
If you would rather sink your teeth into the subject without the potential (over)simplification, bias and distortion prevalent in textbooks and commentaries, and if exploring related philosophical themes beyond gender theory is of interest to you, these are the first books I recommend:
Three Essays on the Theory of Sexuality (Sigmund Freud)
The Second Sex (Simone de Beauvoir)
The History of Sexuality (Michel Foucault)
Gender Trouble (Judith Butler)
Bodies That Matter (Judith Butler)
Undoing Gender (Judith Butler)
Embodied Selves (Stella Gonzalez-Arnal, Gill Jagger, Kathleen Lennon)
If you are not well-acquainted with philosophy, some of these works may seem a bit obscure, even deliberately obtuse. Much of the philosophy of gender studies is rooted in continental philosophy, which is not for everyone but can be introduced and discussed without too much difficulty if all you need is some background information and some familiarity with key figures and peculiar terms. You may also struggle if you have only an Anglo-American picture of linguistics, as another central theme in gender studies is rather the continental variant of linguistics comprised by structuralism and semiotics. I recommend the following books to give a broader, philosophical and linguistic background to the above texts:
The World, The Flesh and The Subject (Kathleen Lennon, Paul Gilbert)
Structuralism: An Introduction (David Robey ed.)
A Course in General Linguistics (Ferdinand de Saussure)
Finally, some familiarity with Karl Marx would be useful but not essential.