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Celtic will host defending champions Real Madrid when the Champions League gets under way on 6 September.
Uefa has confirmed the fixture list for this season's competition following Thursday's draw.
Chelsea travel to face Dinamo Zagreb earlier that day, in one of two 17:45 BST kick offs, and Manchester City are at Sevilla at 20:00 BST.
Three more British clubs, Liverpool, Rangers and Tottenham, start their campaigns the following day.
Rangers go to Ajax for a 17:45 kick-off on 7 September, while Liverpool are at Napoli at 20:00 with Tottenham kicking off at the same time at home to Marseille.
Premier League and Scottish Premiership runners-up Liverpool and Rangers are both in Group A and their first meeting will be on matchday three at Anfield at 20:00 on 4 October.
The return fixture at Ibrox takes place the following week, at 20:00 on 12 October.
The last group stage games take place on 1 and 2 November.
The final will be held at the Ataturk Olympic Stadium in Istanbul, Turkey, on 10 June 2023.
In the Europa League, the opening round of fixtures on 8 September see Arsenal travel to FC Zurich for a 17:45 kick-off while Manchester United play Real Sociedad at home at 20:00.
Hearts face Istanbul Basaksehir at Tynecastle at 17:45 the same day in the Europa Conference League, with West Ham playing FCSB of Romania at home at 20:00.
6 Sep - 17:45 Dinamo Zagreb v Chelsea
6 Sep - 20:00 Celtic v Real Madrid
6 Sep - 20:00 Sevilla v Manchester City
7 Sep - 17:45 Ajax v Rangers
7 Sep - 20:00 Napoli v Liverpool
7 Sep - 20:00 Tottenham Hotspur v Marseille
13 Sep - 17:45 Sporting v Tottenham Hotspur
13 Sep - 20:00 Liverpool v Ajax
13 Sep - 20:00 Rangers v Napoli
14 Sep - 17:45 Shakhtar Donetsk v Celtic
14 Sep - 20:00 Chelsea v Salzburg
14 Sep - 20:00 Manchester City v Borussia Dortmund
4 Oct - 20:00 Liverpool v Rangers FC
4 Oct - 20:00 Eintracht Frankfurt v Tottenham Hotspur
5 Oct - 17:45 RB Leipzig v Celtic
5 Oct - 20:00 Chelsea v AC Milan
5 Oct - 20:00 Manchester City v FC Copenhagen
11 Oct - 17:45 FC Copenhagen v Manchester City
11 Oct - 20:00 AC Milan v Chelsea
11 Oct - 20:00 Celtic v RB Leipzig
12 Oct - 20:00 Rangers v Liverpool
12 Oct - 20:00 Tottenham Hotspur v Eintracht Frankfurt
25 Oct - 17:45 Salzburg v Chelsea
25 Oct - 20:00 Celtic v Shakhtar Donetsk
25 Oct - 20:00 Borussia Dortmund v Manchester City
26 Oct - 20:00 Napoli v Rangers
26 Oct - 20:00 Ajax v Liverpool
26 Oct - 20:00 Tottenham Hotspur v Sporting
1 Nov - 20:00 Liverpool v Napoli
1 Nov - 20:00 Rangers v Ajax
1 Nov - 20:00 Marseille v Tottenham Hotspur
2 Nov - 18:45 Real Madrid - Celtic
2 Nov - 20:00 Chelsea - Dinamo Zagreb
2 Nov - 20:00 Manchester City v Sevilla
8 Sep - 17:45 FC Zurich v Arsenal
8 Sep - 20:00 Manchester United - Real Sociedad
15 Sep - 17:45 Sheriff Tiraspol v Manchester United
15 Sep - 20:00 Arsenal v PSV Eindhoven
6 Oct - 17:45 Omonoia v Manchester United
6 Oct - 20:00 Arsenal v Bodo/Glimt
13 Oct - 17:45 Bodo/Glimt v Arsenal
13 Oct - 20:00 Manchester United v Omonoia
27 Oct - 17:45 PSV Eindhoven v Arsenal
27 Oct - 20:00 Manchester United v Sheriff Tiraspol
3 Nov - 17:45 Real Sociedad v Manchester United
3 Nov - 20:00 Arsenal v FC Zurich
8 Sep - 17:45 Hearts v ?stanbul Basaksehir
8 Sep - 20:00 West Ham United v FCSB
15 Sep - 20:00 RFS v Hearts
15 Sep - 20:00 Silkeborg v West Ham United
6 Oct - 17:45 Anderlecht v West Ham United
6 Oct - 20:00 Hearts v Fiorentina
13 Oct - 17:45 Fiorentina v Hearts
13 Oct - 20:00 West Ham United v Anderlecht
27 Oct - 20:00 Hearts v RFS
27 Oct - 20:00 West Ham United v Silkeborg
3 Nov - 15:30 ?stanbul Basaksehir v Hearts
3 Nov - 20:00 FCSB v West Ham United
