The first full week of the Edinburgh Festival means there’s a wealth of cultural delights to indulge in.

Here we take a look at some recommended shows for the next seven days.

Monday: Alan Cumming Sings Sappy Songs

The Scottish Broadway star comes home for a late-night residency at The Hub. The Olivier Award-winning Cumming sings a selection of his favourite songs from artists as diverse as Kurt Weill and Noël Coward, Stephen Sondheim and Rufus Wainwright, Lady Gaga and Katy Perry. (The Hub, until 27 Aug, 10.30pm, more info)

Tuesday: Sofie Hagen – Shimmer Shatter

The Danish comedian was one of the highlights of last year’s Fringe, and won Best Newcomer in the Foster’s Comedy Awards. However, she manages to justify the hype in her new show – still part of PBH’s Free Fringe – which is another deeply personal yet ultimately uplifting exploration of depression, relationships and childhood. (Liquid Room Annexe, until 28 Aug, 7.50pm, more info)

Wednesday: Yorkston/Thorne/Khan

A trio of musical talents converge at this special Edinburgh International Festival event. Folk singer-songwriter James Yorkston, Indian classical singer and saragi player Suhail Yusuf Khan and jazz bassist Jon Thorne showcase work from their inventive and original debut album Everything Sacred. (The Hub, 10 Aug, 9.30pm, more info)

Thursday: Sam Simmons – Not a People Person

Bizarrely funny gags, surreal sketches and inventive prop use led to Spaghetti for Breakfast being awarded the Fosters Best Comedy Show last year. His new show Not a People Person‘s formula is much the same, packed with scenes only Simmons’ pleasantly deranged mind could devise. (Underbelly Potterow, until 28 Aug, 8.15pm, more info)

Friday: Lemons Lemons Lemons Lemons Lemons

What if there was a limit on how many words we could say in our lifetime? This playfully titled play from Walrus, written by Sam Steiner, explores this premise in the context of social media and modern relationships. (Summerhall, until 28 Aug, 12.10pm, more info)

Saturday: Craig Campbell – Easy Tiger

In ‘Easy Tiger’ Craig Campbell puzzles over the intricacies and oddities of life in the UK as a Canadian, dissecting the standoffish British psyche and regaling tales of passive aggressive hospitality. (The Stand, until 28 Aug, 10pm, more info)

Sunday: David O’Doherty

A true Fringe favourite, O’Doherty tickles audiences with his whimsical songs, using piano skills that he picked up from a brief career as a jazz musician. The Irishman’s ability to turn an everyday incident into an epic tale of Odyssean proportions is remarkable, most notably linking novelty candles to his great grandfather’s role in the Easter Rising. (Assembly Hall, until 28 Aug, 7.30pm, more info)