This is one of the best search tools available -you simply enter the details and you will be presented with tabulated data. It allows you to search by airport code, city, or nearby airports which is excellent since sometimes flying from 1 to smaller airports offer the cost advantages in terms of taxes and fees. So, if flying from Indian, select a central airport, for example Hyderabad and select airports in 1000 mife radius, so it includes airports like Mumbai, Bangalore, Chennai as well. Then go on to the next parameter. One of the interesting feature is that it allows you to check fares for upto a month forward – so you get a range of air fares to compare thus enabling you to find the lowest fares. You can also filter as per your airline choice and stopovers. The color coded bars make comparison of flights easy. Please note that tickets cannot be purchased directly from ITA Software.
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Fly.com, Kayak.com, Hipmunk.com etc. These are meta search engines which search with multiple sites and tabulate search results that can be compared. They do not have booking engines i.e. they will not sell tickets themselves, but they will provide links to other (affiliate) sites that do sell like Expedia.com or direct booking with the airlines. [These meta search engines I aggregators earn by referral I affiliate income wherein every search made through their site may lead a prospective passenger to click the link, book the ticket and Kayak gets paid a percentage of the sale.)
Google Flights. It is faster, but has less options for you to input. It is alright if you need to search quickly especially for a single ticket.
MakeMyTrip, Yatra, Expedia, TraveSocity etc. These are online travel agencies selling air tickets that you can purchase directly from the airline website [which many times offer less price). But you may consider buying tickets from these online agencies for two reasons -firstly, sometimes search results show that flying multiple airlines will be more cost beneficial than flying a single airline throughout. This is especially if you fly multi-city routes. Secondly, these agencies sometimes offer deals or promotional fares.