SCOTLaND'S busiest airport clocked up new records last month, with the most passengers since civilian flights started there 64 years ago.  Edinburgh handled nearly one million travellers in July, and Saturday the 16th was the airport's single busiest day, with more than 36,000 passing through the terminal - 4,000 above the month's average.  The records, attributed to an increase in international flights and routes, helped to bolster Edinburgh's position as Scotland's fastest-growing large airport.  It follows the airport achieving its busiest ever March, april and June this year.  However, Glasgow and aberdeen, the country's two other main terminals, benefited from route growth, too, and saw passenger numbers rise for a seventh successive month.  Glasgow finally halted a six-year decline in annual passenger numbers, but UK traffic at all three airports continued to fall.  Edinburgh's passenger total last month increased to 992,500, up 3.3 per cent compared with the same month in 2010, according to figures published by owner Baa.  That accelerated the airport's annual growth to 5.7 per cent and nearly 9.2 million passengers - a stark turnaround when the total was shrinking by 3 per cent a year ago.  EasyJet and Ryanair, the main carriers at Edinburgh, have both added new European routes and expect to carry nearly 4m passengers from the airport between them this year.  airport managing director Kevin Brown said: "This fantastic performance is testament to the continued appeal and resilience of Edinburgh as a place in which to live, work and visit and to the hard work and dedication of the team at Edinburgh airport. We're continually adding new routes and upgrading our facilities."  an airport spokesman added: "July's success was driven in the main by international passengers. Our scheduled European market has performed extremely well, showing the benefit of our strategy to increase Edinburgh's links across the continent."  aberdeen recorded the largest passenger increase of the three main airports last month, up 8.7 per cent to 301,000.  Managing director Derek Provan said it had also been fuelled by route growth.  He said: "We are delighted with our performance in July and particularly pleased with the strong demand for international services.  "This reflects the introduction of new routes such as Baku with azerbaijan airlines. There have also been other domestic routes come on stream, for example the EasyJet service to Gatwick."  Glasgow airport's passenger total grew slightly last month, by 0.5 per cent to 793,200, halting a decline that started in 2005. It was overtaken for passenger numbers by Edinburgh four years ago. July's growth was largely attributed to the arrival of Jet2, whose seven routes contributed to the airport's European traffic increasing by nearly half.  Glasgow also attracted more transatlantic passengers, especially from the United States.  Glasgow managing director amanda McMillan said she was encouraged but still cautious about the airport's performance, particularly since BMI had axed its r