This book constitutes the proceedings of the First International Joint Conference on Quantitative Evaluation of Systems and Formal Modeling and Analysis of Timed Systems, QEST+Formats 2024, which took place in Calgary, AB, Canada, during September 2024. This year the 21th International Conference on Quantitative Evaluation of SysTems (QEST 2024) and the 22nd International Conference on Formal Modeling and Analysis of Timed Systems (FORMATS 2024) joint forces and took place as part of the CONFEST 2024 umbrella conference.  The 19 full papers presented in this book were carefully reviewed and selected from 33 submissions. They deal with up-to-date topics in quantitative evaluation and verification of systems, focusing on fundamental and practical aspects of systems with quantitative nature, such as probability, timing, and cost, and modeling, design and analysis of computational systems.