Warning. University of Warwick is not in Warwick (though it is in the county Warwick or Warwickshire). In reality, it is (essentially) in Coventry. (But there is also a University of Coventry, which is different and in a different part of Coventry.)
Accommodation. Most probably, you will be accommodated in one of the hotels on campus or in Kenilworth, which is about 10 minutes by bus (no 11) from the university. Note that a surprising number of taxi drivers (even from the Coventry area) do not know Kenilworth well (this is based on remarks of others as well as my own observation).
Coventry is also on the line ... - Reading - Oxford - Leamington Spa - Coventry - ... However, it may be more convenient to go to Leamington Spa only (some trains do not go to Coventry) and then take a bus or taxi (15-25 pounds) from there to Kenilworth or Warwick University.
See National Rail Enquiries for timetables and other buying options such as The Trainline, etc.
Birmingham International Airport, BHX. Direct flights from a number of European cities and from Newark EWR. A taxi from Birmingham Airport to the Mathematics Institute or to Kenilworth should be in the region 20-30 pounds. Alternatively, make your way to the Birmingham International Railway Station and take a train to Coventry Railway Station (frequent service, about 10 minutes journey, cost 1.50 -- 2.10).
Coventry Airport, CVT. Direct flights from some European cities. A taxi from Coventry Airport to the Mathematics Institute or to Kenilworth should be in the region 20-30 pounds. Alternatively, take a bus to Coventry and then a bus to University or Kenilworth.
East Midlands Airport, EMA. Direct flights from some European cities. A National Express bus to Coventry Pool Meadow Bus Station (infrequent service).
Manchester Airport, MAN. Direct flights from some European cities. Trains (with one or more changes) from Manchester Airport to Coventry or to Leamington Spa, see National Rail Enquiries.
Heathrow Airport, LHR. There seems to be no canonical route. All of the following take about 2-3 hours.
Via London: By the underground to Euston Station (with one change, eg at Green Park to Victoria Line) or by Heathrow express to Paddington and there change to underground to Euston Station. (The latter may cost significantly more but should be faster.)
Via Watford: The Green Line bus 724 to Watford Junction, from where there are direct trains to Coventry. The timetable for 724 may be found at traveline south east.
Via Reading: Similar to the above, the RailAir bus goes from the Central Bus Station to Reading, from where there are direct trains to Leamington Spa (and Coventry).
Via Oxford: Similar to the above, "theairline" run by the Oxford Bus Company goes from the Central Bus Station (and from terminal 5) to Oxford, from where there are direct trains to Leamington Spa (and Coventry).
By Coach: The National Express buses take about 2 hours from the Heathrow Central Bus Station to Coventry Pool Meadow Bus Station. Departure times are distributed according to an unclear law. One can buy tickets on their web page and print them. (However, an "amendment charge" in case of late arrival may be significant; see their info.)
Gatwick Airport, LGW. Again, there seems to be no canonical route. Perhaps the most convenient may be to go by train via Watford (the railway station is at the airport, hourly direct trains to Watford Junction). One can also go via London, or take a National Express bus.
Luton Airport, LTN. A National Express bus to Coventry Pool Meadow Bus Station (infrequent service) or train to London St Pancras Station or Kings Cross Station; both are within a walking distance from Euston Station.
Stansted Airport, STN. A National Express bus to Coventry Pool Meadow Bus Station (infrequent service) or train to Tottenham Hale followed by underground (Victoria Line) to Euston Station.
Megabus from London Victoria, Greenline Coach Station to Coventry, Cannon Park (a short walk from the campus). Tickets can be bought only on their website and are not refundable.
11: Coventry Pool Meadow Bus Station - Coventry Railway Station (see below for location of bus stop) - Warwick University - Kenilworth - Leamington Spa.
12: Coventry Pool Meadow Bus Station - Coventry Railway Station (see below for location of bus stop) - Warwick University.
Warning. Accepts exact change only. Other passengers usually unable or unwilling to help. Examples of recently paid fares (note that fares tend to increase without much warning and that other buses may have very different fares):
Coventry - Warwick University: 1.80.
Coventry - Kenilworth: 1.80.
Warwick University - Kenilworth: 1.80.
Bus number W1c (convenient, quick, stops also in front of the station, but only one per hour): Coventry Railway Station - Warwick University. (In the opposite direction it is much slower.)
Buses number W1a and W6 (convenient, quick, some buses stop also in front of the station, but only one per hour): Warwick University - Coventry Railway Station. (In the opposite direction it is much slower.)
Bus number U1: Warwick University - Leamington Spa.
Buses not mentioned above or in these links include Stagecoach number 16 (quick journeys between Coventry railway station and Warwick university, but doesn't go very often).
The bus stop at the Coventry Railway Station is not in front of the station (except for rare W1c) and is not obvious to find. A simple algorithm is: once you leave the platforms, turn left whenever walls or fences allow you to until you reach the stairs leading to the bridge above the rails. The bus stop is on the bridge.
I would be obliged to anyone who lets me know a similarly simple algorithm for recognising the railway station bus stop when returning from the University or from Kenilworth. Currently, the only algorithm I know of is asking the driver to tell you (which has been reported not to be fully reliable), asking fellow passengers or noticing King Henry VIII School on your left: leave the bus once you passed it.
On rare occasions you may meet drivers of buses number 11 and 12 willing to accept less than the official fare, more commonly you meet drivers willing to accept more. Buses run by other companies usually give change.