Abstract This guide explores asymmetric-key cryptography (AKC) as part of quantum-safe cryptographic practices using IBM Q. Asymmetric cryptography underpins many secure network communications today, providing mechanisms for key exchange, digital signatures, and authentication. Unlike symmetric-key cryptography, AKC uses a public-private key pair, enabling secure communications without sharing a secret key. The lesson covers: Fundamentals of asymmetric-key cryptography. Practical applications, including RSA, DSA, and elliptic curve algorithms. Python examples demonstrating key generation, encryption/decryption, and digital signatures. Evaluation of security considerations against classical and quantum computing attacks. Discussion of potential vulnerabilities and mitigation strategies in the quantum era. By integrating theory with hands-on experimentation on IBM Q, developers gain practical skills to implement asymmetric-key cryptography while understanding the impact of emerging quantum threats and preparing quantum-resilient secure systems.