ICAO issues recommendations/rules/statutes/something? that standardizes the regulations for international air travel world-wide.
What are these "rules" officially called and where can they be found? Are they available on the internet?
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ICAO publishes and maintains 19 Annexes to the Chicago Convention. They pertain to all matters in aviation and provide the framework for national legislation in each of the member countries in the form of Standards and Recommended Practices (SARP).
In addition to the 19 Annexes, ICAO also produces more detailed guidance in the form of Procedures for Air Navigation Services (PANS): PANS-ABC, PANS-OPS, PANS-ATM. These are also usually referenced by their Doc number: 2007, 8168, 4444, etc
In addition to the PANS, for specific regions of the world ICAO publishes Regional Supplementary Procedures (SUPP) to incorporate regional variants/requirements.
Any ICAO contracting state may have local legislation different from SARP/PANS, but is obliged to notify ICAO of these differences. You will find these differences in the country's AIP section GEN.
Getting electronic copies of these documents is a bit more difficult. ICAO sells these documents for a very 'aviation' price. Some CAA's and institutions will provide electronic copies in PDF form, but they will most likely be out of date and their legality is suspicious at best. Welcome to the world of international law.