Linguistic Criticisms focus on the language of the text itself, with "language" referring also to internal structures, signs, styles, etc.
There are five main types:
1. Formalism
2. New Criticism
3. Structuralism & Semiotics
4. Post-Structuralism & Deconstructionism
5. Reader-Response Criticism
For more information, I recommend Culler's Literary Theory: A Very Short Introduction.