Rain ***

Without ****

Hyperactive ***

Ponies Don’t Play Football ***

Amú/Cótaí Dearga ***/****

Quad ****

In the closing image of the absorbing dance documentary Rain, the camera lingers on a night-time shot of an illuminated Paris Opera Theatre. But we imagine that the dazzling glow is actually emanating from within.

The film follows Ballet de l'Opéra de Paris's first engagement with modern dance choreographer Anne Teresa De Keesrmaeker and her classical trained Rosas company to present her mesmeric work Rain. It's very much an inside job for directors Olivia Rochette and Gerard-Jan Claes. Their focus is in the studio, on the doing and redoing, and with the dancers as they audition, learn, unlearn and are cajoled into thinking and moving differently.

To a subtly insistent score, we follow down dark hallways, appreciate bruised and bandaged feet and eavesdrop on snatched calls between the team and the dancemaker as they juggle domestic and professional lives. The hesitant finally becomes fluent as the dancers embrace De Keersmaeker’s invitation to relax and infuse gestures with their own personalities.

Without is also a site -specific visual journey with an unfamiliar community of performers. Rain remapped a dance idiom; Rosemary Lee's work with Echo Echo Dance Company remapped the contours of a city. In this installation for Derry City of Culture 2013, the viewer spins around the seven screens at Rua Red Gallery as stone and brick slowly swarm with black and white figures in motion – men, women and children on foot, bike, wheelchair.

With the wind billowing their loose white shirts, this community of 400 are dispersed around the squares of town hall and cathedral, of housing estates, city walls, parks and bus-fuelled streets. They dance in twos and threes, like a pop-up citizenry on the move, crouching and running, creating shapes of a siege, a protest or a lost childhood game.

Sometimes the figures are dissolved into their landscape and you long to see their familiar shapes turn a corner, arms raised, mirroring the open and ever commanding arms of the Craigavon bridge.

Raising their arms and inhabiting an open space seems to come naturally to the five athletic performers of Hyperactive, as they transform gravelly Wolfe Tone Square into a sandpit teeming with dance energy and boyish glee. Under John Scott's instruction, their red tennis shoes and immaculate whites are soon bearing all the marks of the get-down-and-dirty dance. It is highly charged, wonderfully high-octane exhibitionistic fun, an entertaining sugar rush for all involved.

More than one spoonful of sugar is certainly fuelling the antics of Ponydance. Always hovering on the edges of cabaret and burlesque, they may have found their night-town niche by adding a live band to the mix. For Ponies Don't Dance, the Project stage is heaving, hyperactive and riding high. With comical self-deprecating dance, the Ponydancers' trademark sheer physicality and breakneck speed cover a few near misses. Combined with the music, this creates an infectious, unself-conscious atmosphere. There will be no spoilers here for the opening salvo of ponies and panties; this show should return.

Another candidate for a reprisal is a hidden gem of the festival: Ciotóg's Cótaí Dearga, part of a double bill presented at the Civic Theatre. Amú, Robert Jackson's opening solo, is well realised, but it is eclipsed by this duet in which choreographer Ríonach Ní Néill also performs. She muses, delves and creates a highly original work drawing on the red skirts and shawls worn by the traditional women of the Aran Islands.

Evoking Paul Henry or Sean Keating's women gathering seaweed, the dance skilfully manoeuvres us into a secret seashore life, young women playfully refashioning their vivid skirts,swirling like distant cousins in their dervish dances. They gambol and stretch, then veil their heads and faces in the thick red cloth. We and they imagine other dreams and freedoms. The pure choral sean-nós song score, with Arabic atonal swoops and falls, imaginatively connects us to other worlds.

Connecting the worlds of mathematics, Samuel Beckett and contemporary dance is an intriguing piece called Quad. In it, Pan Pan Theatre and Irish Modern Dance Theatre collaborate with mathematician Conor Haughton to excavate and reimagine the choreographic and mathematical puzzle of Beckett's work Quad. A blackboard, Beckett scholar Nick Johnson and Haughton's droll wizardry add to the illumination and experiment. Answer: The permutations are not limitless, and the magic number is five.

In Quad, four dancers in distinctively coloured hoodies walk sequentially and purposefully around the four corners of the spaces, on the edges and in near deliberate collisions on the diagonals. They acknowledge the presence of others in their deft swervings, each with their own identity tags of timing, lighting colour and sound keys.

In Quad 2, a version imagined by Beckett a thousand years on, the colours and sounds are bleached from the piece, the dancers now walking to a slow, internal rhythm, with no physical encounter but with the ritual still in place. In Quin, the show's playful proposal for perfection, the dancers – helmeted like a group of motorbike couriers – move as if following individual GPS systems. The hexagonal space allows for the maths, but Beckett is right: the ritual is erased, and there is no possibility of human connection.

That possibility and need for human interaction tugs at the corners of several other shows this year: the isolation of Tundra; the inhospitality of Dan Canham's Fen; and that final image of the two dancers on parallel ice floes off Russell Maliphant's Still Current, before they melt into one.