She’s only 30, but Mae Martin has been at this comedy lark for a long time.

Wondering what on earth to choose between as you tramp the streets of the festival? These are our highlights so far.

STANDUP

Athenu Kugblenu, Underbelly Med Quad ★★★ Strong debut hour of political and identity comedy

Ingrid Oliver ★★★★ 

Ingrid Oliver is an old Edinburgh hand as one half of the sketch duo Watson and Oliver, but this is her debut solo show, and a very fine one it is. The set-up in Speech! is that she plays various characters giving speeches – among them a nervous TED-talker, a man leading an improv class, and a boorish student-union activist who wants to no-platform everybody ("As students we shouldn't have to engage with other people's opinions").

Hannah Gadsby ★★★★

This is Hannah Gadsby's last show, she tells us. Not because she has stopped being funny (she most definitely hasn't, as the laugh count in this show attests), but because making comedy out of her life experience has become toxic for her.

Tom Allen ★★★★

Tom Allen is celebrating his 10th year at the Fringe, and he appears to be having a ball – and so do we. He bounds on stage full of energy and does a fantastically strong 10 minutes' interaction with the audience, and when he finds comedy gold in the front row with a management consultant, a nurse on a liver ward and a judge, he dextrously weaves details of their lives into the show.

Kiri Pritchard-McLean ★★★★

Appropriate Adult has an unlikely subject for comedy – Kiri Pritchard-McLean's work with vulnerable teenagers. But it proves rich territory as she recounts her relationship with one in particular, 15-year-old “Harriet”. Don't worry, it doesn't pose an ethical issue, as the comic, rather than the child, is the butt of the jokes – of which there are plenty.

Tiff Stevenson ★★★★

“I identify as a 10!” Tiff Stevenson tells us in Bombshell. It’s a strong opener, particularly as she follows with: “And if you don’t agree you’re beauty-phobic.” It’s not to boast, though, more marking her territory in a show about the shifting sands of modern sexual politics. Why should women identify with a male view of the world?

The Big Sick is an enchanting film from the Judd Apatow comedy production line. Don’t be put off by the terrible title. There are two forms of sickness on display in the story of Kumail Nanjiani, a Pakistani American who plays himself in his own autobiographical romantic comedy.

Were ordinary folk to plunder their lives for comedy, most of us would be sadly lacking in any topics worthy of analysis, let alone laughs. But Russell Brand, who every few years appears to reinvent himself – from drug addict to stand-up comic, from sex addict to husband, from anarchist to social campaigner, to name a few reboots – can in no way be described as ordinary.

Ricky Gervais enters the stage after recordings of some the great (and not so great) men of history – including Winston Churchill, Martin Luther King and Adolf Hitler. And then there's a portentous introduction – are we then going to hear some deep philosophical insights tonight? Well not so much, more chatty and relaxed riffing, with some of his most personal material yet.