This season, English champions Manchester City are making their third appearance in UEFA’s top competition for clubs – the Champions League (formerly known as the European Cup).

Their previous showings were not something to shout about as the Citizens suffered early exits. When the 2012-13 draws were made in August, Man. City came up in the toughest group but they still have high hopes of advancing.

Man. City’s short history in the European Cup reads:

1968-69 (first round): Fenerbahce − home 0-0, away 1-2 (aggregate 1-2).

2011-12 (group matches): Napoli − home 1-1, away 1-2 (one point).

2011-12 (group matches): Bayern Munich − away 0-2, home 2-0 (three points).

2011-12 (group matches): Villarreal − home 2-1, away 3-0 (six points).

On the opening day of the 2012-13 Champions League group phase earlier this month, Manchester United and Arsenal did well to collect their first three points.

United beat Galatasaray 1-0 (Carrick) at Old Trafford and the Gunners beat Montpellier away 2-1 (Podolski, Gervinho).

The Citizens were twice in the lead away at Real Madrid but lost 3-2.

Perhaps, the biggest upset came from Chelsea. The European champions led 2-0 against Juventus (Oscar 2) at Stamford Bridge but the Serie A winners hit back to equalise after the Blues committed some errors at the back.

Oscar’s second goal for the Blues is an early candidate for goal of the season.

Celtic, the other British team in the competition, could not go beyond a 0-0 draw against Benfica at home.

Next Tuesday, Chelsea will be on their travels as they head to Denmark to play minnows FC Nordsjaelland.

The Superliga side are known as the Wild Tigers. This is their fourth appearance in UEFA competitions but their first in the Champions League after winning the domestic championship last season.

Chelsea will play a team from Denmark for the fourth time.

2010-11 (Champions League, second round KO): FC Copenhagen − away 2-0, home 0-0 (2-0 aggregate).

1998-99 (Cup Winners’ Cup, second round): FC Copenhagen − home 1-1, away 1-0 (2-1 aggregate).

1958-60 (Fairs Cup, first round): Frem − away 3-1, home 4-1 (7-2 aggregate).

Romanian champions CFR Cluj will have home advantage against Manchester United next week. This is their fourth appearance in the Champions League.

Cluj met Chelsea in a group match in 2008-09 with the Blues gaining four points after an away draw and a home win.

United have met Romanian opposition twice.

In 2004-05, in a qualifying round match, they beat Dinamo Bucharest at home and away. Last season, the Red Devils faced Otelul Galati in the group stages, winning both ties to obtain six points.

In Group E, Celtic play away in Moscow against Spartak on Tuesday.

Four years ago the two sides met in the same competition but in the qualifying round. The outcome was locked at 2-2 after both teams drew their home tie 1-1. Celtic went through 4-3 on penalties.

Manchester City will take on Borussia Dortmund, the German champions, on Wednesday at the Etihad Stadium. The Citizens have never been beaten at home by German sides:

2008-09 (UEFA Cup quarter-final): Hamburg 2-1.

1978-79 (UEFA Cup quarter-final): Borussia M’gladbach 1-1.

1969-70 (Cup Winners’ Cup semi-final): Schalke 5-1.

In-form Arsenal are optimistic of going far at home and in Europe this season as manager Arsene Wenger is looking to make up for the team’s lack of silverware in the last seven years.

In Group B, the Gunners host Olympiakos at the Emirates Stadium.

Their last two meetings with Greek sides were against the same Olympiakos in the Champions Lea-gue group phase.

In 2009-10 Arsenal took three points after a victory at home and in 2011-12 the story repeated itself when the six points at stake in the group games were shared.

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