Andy Murray return to Wimbledon could see him face his older brother Jamie in the third round of the men’s doubles.
Rafael Nadal is in the same half of the men’s singles as eight-time champion Roger Federer – and could play Nick Kyrgios in the second round.
British men’s number one Kyle Edmund, seeded 30th, will play Jaume Munar of Spain in the first round on Monday.
Johanna Konta, Britain’s leading female player, will play Romanian qualifier Ana Bogdan on Tuesday.
Defending men’s champion Novak Djokovic, who is the top seed, will play Germany’s Philipp Kohlschreiber in the first match on Centre Court at 13:00 BST on Monday.
Last year’s women’s champion Angelique Kerber, seeded fifth, starts against fellow German Tatjana Maria on Tuesday.
Kerber could then face American 23-time Grand Slam winner Serena Williams, who opens against Italian qualifier Giulia Gatto-Monticone, in the last 16.
New world number one Ashleigh Barty will play China’s Zheng Saisai, ranked 43rd, and is projected to face Spanish 2017 champion Garbine Muguruza in the third round.
American 15-year-old Cori Gauff, the youngest player to qualify for the main Wimbledon draw since the Open era began in 1968, has been rewarded with a first-round match against five-time champion Venus Williams, who is 24 years older than her compatriot.