- Mathematical Logic by Stephen Cole Kleene: This book provides a comprehensive introduction to mathematical logic and covers topics such as propositional logic, predicate logic, set theory, and proof theory.
- Mathematical Logic by George Tourlakis: This book offers a rigorous and detailed treatment of mathematical logic, including topics like formal languages, axiomatic systems, and model theory.
- Introduction to Mathematical Logic by Elliott Mendelson: This book is a classic text on mathematical logic and covers various topics including propositional and predicate logic, set theory, and computability theory.


- EduRev (www.edurev.in): EduRev offers a wide range of study materials, notes, and practice questions specifically tailored for the UPSC Mathematics Optional subject exam. They provide comprehensive coverage of the mathematical logic section along with solutions and explanations.
- Math Stack Exchange (math.stackexchange.com): This online community allows students to ask questions and get answers from experts in the field of mathematics. It is a great resource for clarifying doubts and understanding complex concepts related to mathematical logic.


- Solving previous year question papers is essential for understanding the exam pattern and the types of questions asked. It helps in identifying the important topics and areas that require more focus. UPSC Mathematics Optional subject exam previous year question papers can be obtained from the official UPSC website or other trusted sources.


- NPTEL (www.nptel.ac.in): NPTEL provides free online video lectures on various subjects, including mathematical logic. These lectures are delivered by experienced professors and cover the fundamentals as well as advanced topics of mathematical logic.
- Youtube: There are numerous educational channels on Youtube that offer video lectures on mathematical logic. Some popular channels include Khan Academy, MIT OpenCourseWare, and Numberphile.


- Joining study groups or participating in online discussion forums related to UPSC Mathematics Optional subject can be immensely helpful. Interacting with fellow aspirants allows for the exchange of ideas, clarification of doubts, and gaining different perspectives on mathematical logic.

By utilizing these study materials, aspirants can develop a strong understanding of mathematical logic and successfully prepare for the UPSC Mathematics Optional subject exam.