This monograph provides a comparative analysis of FALCON and SOLMAE, two PQC signature schemes, within the context of quantum computing advancements. FALCON, selected by NIST as a PQC standard, is recognized for its pioneering role, while SOLMAE offers practical advantages, such as simpler implementation and improved performance. Both schemes ensure message integrity and long-term security against quantum-based threats but require deeper algebraic understanding compared to traditional cryptographic methods like DSA and ECDSA. Key Python-based modules of FALCON and SOLMAE are examined to aid understanding, focusing on the generation and verification of security parameters for NIST level of security I and V configurations. As a future work, the monograph emphasizes the need for ongoing performance optimization and cross-platform security to meet the evolving demands of PQC.