The HHH Workshop, held in Dubrovnik in July 2023, focused on the study of triple-Higgs production, a process that is extremely rare and challenging to observe at the LHC. The discovery of the Higgs boson confirmed the Standard Model (SM) predictions, but the full form of the Higgs potential, including the triple and quartic scalar couplings, remains to be determined. The workshop discussed experimental and theoretical progress in measuring multi-scalar final states, with a focus on three SM-like scalar bosons at 125 GeV, as well as other possibilities. It emphasized the importance of understanding the Higgs potential for exploring physics beyond the SM, particularly in the context of the electroweak phase transition and matter-antimatter asymmetry. The HHH process is highly suppressed due to destructive interference between diagrams, making it difficult to observe at the LHC. However, future proton-proton colliders operating at higher energies, such as 100 TeV, could significantly enhance the production cross sections. The workshop also discussed the use of the κ-framework to model new physics effects in the Higgs potential, allowing for the study of deviations from SM predictions. The κ parameters, κ3 and κ4, modify the cubic and quartic Higgs couplings, and their values can be constrained through experimental data. The workshop highlighted the importance of precise measurements of Higgs couplings, particularly the quartic coupling, which is crucial for understanding the Higgs potential. It also discussed the challenges of b-tagging and flavor assignment in the context of Higgs production, which are essential for identifying signal events. The study of triple-Higgs production can provide insights into new physics scenarios, including extended scalar sectors and resonant contributions. The workshop concluded with a consensus that the discussions should continue, and a second HHH workshop is planned for 2025. The results of this workshop aim to serve as a catalyst for future theoretical and experimental work on HHH production, potentially leading to the first experimental results on triple-Higgs production. The workshop also emphasized the importance of advanced machine learning techniques and high-level variables in improving the analysis of Higgs production processes. Overall, the HHH Workshop provided a comprehensive overview of the current state of research on triple-Higgs production and its implications for understanding the Higgs potential and physics beyond the Standard Model.The HHH Workshop, held in Dubrovnik in July 2023, focused on the study of triple-Higgs production, a process that is extremely rare and challenging to observe at the LHC. The discovery of the Higgs boson confirmed the Standard Model (SM) predictions, but the full form of the Higgs potential, including the triple and quartic scalar couplings, remains to be determined. The workshop discussed experimental and theoretical progress in measuring multi-scalar final states, with a focus on three SM-like scalar bosons at 125 GeV, as well as other possibilities. It emphasized the importance of understanding the Higgs potential for exploring physics beyond the SM, particularly in the context of the electroweak phase transition and matter-antimatter asymmetry. The HHH process is highly suppressed due to destructive interference between diagrams, making it difficult to observe at the LHC. However, future proton-proton colliders operating at higher energies, such as 100 TeV, could significantly enhance the production cross sections. The workshop also discussed the use of the κ-framework to model new physics effects in the Higgs potential, allowing for the study of deviations from SM predictions. The κ parameters, κ3 and κ4, modify the cubic and quartic Higgs couplings, and their values can be constrained through experimental data. The workshop highlighted the importance of precise measurements of Higgs couplings, particularly the quartic coupling, which is crucial for understanding the Higgs potential. It also discussed the challenges of b-tagging and flavor assignment in the context of Higgs production, which are essential for identifying signal events. The study of triple-Higgs production can provide insights into new physics scenarios, including extended scalar sectors and resonant contributions. The workshop concluded with a consensus that the discussions should continue, and a second HHH workshop is planned for 2025. The results of this workshop aim to serve as a catalyst for future theoretical and experimental work on HHH production, potentially leading to the first experimental results on triple-Higgs production. The workshop also emphasized the importance of advanced machine learning techniques and high-level variables in improving the analysis of Higgs production processes. Overall, the HHH Workshop provided a comprehensive overview of the current state of research on triple-Higgs production and its implications for understanding the Higgs potential and physics beyond the Standard Model.