Introduction:
Preparing for the UPSC Law Optional subject requires a deep understanding of various legal principles and maxims. These principles and maxims serve as guiding tools for interpreting and applying the law. Here are some important legal principles and maxims that you should focus on:

Principles:
1. Doctrine of Stare Decisis: This principle emphasizes the importance of following precedents and maintaining consistency in legal decisions.

2. Principle of Natural Justice: It requires that decisions be made impartially, without bias, and after giving all parties a fair opportunity to present their case.

3. Principle of Equity: This principle ensures fairness and justice in situations where strict application of the law may lead to undesirable outcomes.

4. Principle of Promissory Estoppel: It prevents a person from going back on their promise if the other party has relied on that promise to their detriment.

5. Principle of Res Judicata: It prevents the same matter from being re-litigated between the same parties once a final decision has been reached.

6. Doctrine of Severability: It allows a court to strike down a specific provision of a law while retaining the rest of it, if the provision is found to be unconstitutional.

7. Principle of Constitutional Validity: This principle requires that laws and governmental actions be in accordance with the provisions of the Constitution.

Maxims:
1. Ignorantia Juris Non Excusat: Ignorance of the law is not an excuse. This maxim emphasizes that individuals are expected to know and abide by the law.

2. Actus Non Facit Reum, Nisi Mens Sit Rea: The act does not constitute guilt unless done with a guilty mind. It highlights the importance of establishing criminal intent for an act to be considered a crime.

3. Nemo Debet Esse Judex In Propria Causa: No one should be a judge in their own cause. This maxim emphasizes the need for impartiality and fairness in legal proceedings.

4. Audi Alteram Partem: Hear the other side. It requires that all parties involved in a legal dispute be given an opportunity to present their case before a decision is made.

5. Caveat Emptor: Let the buyer beware. This maxim places the responsibility on the buyer to be cautious and diligent while making a purchase.

6. Volenti Non Fit Injuria: To the willing, no injury is done. It implies that if a person willingly assumes a risk, they cannot later claim compensation for any resulting harm.

7. Expressio Unius Est Exclusio Alterius: The expression of one thing is the exclusion of the other. This maxim suggests that when a law explicitly mentions certain things, it implies the exclusion of others.

Conclusion:
Focusing on these legal principles and maxims will help you develop a strong foundation in the UPSC Law Optional subject. Understanding their nuances and applications will enable you to analyze legal scenarios, interpret statutes, and make well-reasoned arguments. Remember to revise and practice applying these principles to various legal scenarios to enhance your understanding and application skills.