Although liberalism has affected all the branches of Christianity, it does not represent its own branch. Liberalism is more like a virus that infects different parts of the tree and ultimately kills those parts. Historically, that is what we have seen with the mainline Protestant denominations in the United States, although it has also infected Roman Catholicism as well as Eastern Orthodoxy.
Liberalism is related to Progressivism just as an adult is related to a child. The latter inevitably grows into the former.
Here are some important resources for learning about theological liberalism:
Seven Characteristics of Liberal Theology – Kevin DeYoung | A good overview
Liberal Theology – Andrew Hoffecker | Provides the historical background from the Enlightenment forward
Liberal Theology: A Critical Assessment – Thomas Nettles | Examines different areas in light of traditional Christian doctrines
One of the most famous books written on the subject is Christianity and Liberalism. J. Gresham Machen, a conservative theologian in the liberal-leaning Presbyterian Church wrote this important book in 1923. It is just as relevant 100 years later.
Christianity and Liberalism – J. Gresham Machen (PDF download from Archive.org)