This Sunday is traditionally titled the Sunday after Ascension, though these days in some countries has become 'Ascension Sunday' (!). The Gospel is St John 15:26-16:4.
The 1962 Benedictine Office in summary this week
Notes on the rubrics for Ascensiontide can be found here, while more detailed instructions for praying the Office this week can be found in the Ordo for June.
Sunday 1 June - Sunday after the Ascension, Class II
Monday 2 June - Class IV; SS Marcellinus and Peter, memorial [EF: and St Erasmus]
Tuesday 3 June - Class IV
Wednesday 4 June - Class IV [EF: St Francis Caracciolo]
Thursday 5 June - St Boniface, Class III
Friday 6 June - St Norbert, Class III
Saturday 7 June - Whitsun Eve (Vigil of the Pentecost), Class I