The fastest option from Melbourne Airport is to take a taxi. Taxi fares in Victoria vary based on distance, location and time of travel. However, a taxi fare from the airport to The University of Melbourne Parkville campus typically cost somewhere between $50-70 AUD. Please note that additional charges may apply if you travel on public holidays, book in advance, make payment electronically, use toll roads or use a vehicle with five or more passengers. Full details of charges can be found here http://taxi.vic.gov.au/passengers/taxi-passengers/taxi-fares.
Another option is to take the Skybus shuttle bus. Tickets can be purchased online or at self-service kiosks and Skybus ticket booths. A one-way and return fare is $19 AUD and $38 AUD respectively. Skybus operates 24 hours a day between Melbourne Airport and Southern Cross train station in the CBD. A free shuttle service between Southern Cross and participating hotels operates 7 days a week (hours vary during the week). For further information, please consult the Skybus website https://www.skybus.com.au.
The cheapest option is to use public transport. Public transport in Victoria uses the Myki ticketing system. A Myki Visitor Value pack can be purchased from the Melbourne Airport terminal for $14 AUD which includes $8 AUD credit for travel. The recommended route via public transport is to take the route 901 bus to Broadmeadows Station and take an inbound train to Flinders Street station to the CBD. Please note the sign on the bus should say `Frankston'. Further information on the Myki ticketing system, fares and the visitor value pack can be found here https://www.ptv.vic.gov.au/tickets/myki/.