There are many things that intrigue about the life of Leonardo da Vinci, and many theories, some more outlandish than others, have sprung up to explain them. But if da Vinci was appreciated in his lifetime, and acknowledged by both various Italian states and the French king, Francis I, as a genius in many spheres, the larger part of his work was not disseminated in his lifetime. Some 20 paintings were completed by his death in 1519 including the Mona Lisa, The Last Supper and The Virgin and Child with St. Anne, although many were destroyed either during his lifetime or shortly after. But they represent in some ways just the tip of the iceberg of da Vinci's interests, for his life was a slew of unfinished projects and grand plans, all put down on paper in drawings that ranged from indepth anatomical studies to caricatures. Unseen for the larger part by anyone outside his studio, perhaps, or his closest associates during his lifetime, his huge collection was bequeathed to his student Francesco Melzi after his death giving the true measure of this unabashed polymath. Now a large number of these drawings, in the collection of the Queen, are on display at the Palace of Holyroodhouse to celebrate the 500th anniversary of the artist's death.

Da Vinci was born in 1452 near Vinci, close to Florence, and by the age of 20 was working as an artist, eventually in the studio of the sculptor Andrea del Verrochio. Even his earliest works were marked in mirror writing, which, whilst other more clandestine reasons have been posited, was probably simply a result of his being left-handed, to avoid smudging the ink which had just been put down by the pen. Throughout his life he moved from court to court, patron to patron, as wars between Lombardy and France raged, until the final years of his life, when he ended up at the court of Francis I in Amboise as painter, engineer and architect to the King, fully appreciated by a monarch who was so stimulated by da Vinci's insightful presence that he “would only on a few days of the year deprive himself of his company.”

Da Vinci's breadth is astonishing, with the drawings revealing a level of expertise and thought and invention in so many different spheres as to make a near-mockery of the phrase “Renaissance Man”. There are works displayed in this exhibition which are the result of dissections of the human body, a reaching towards and understanding of anatomy that far surpassed that of his peers and yet was still mired in the old beliefs, despite what was presented before his eyes. There are the intricate botanical studies, the exacting studies of the muscles in an arm, or the folds in a piece of material arranged over the human body. There are inventions, diagrams of war games and strategies, instructions on how to construct a gun. There are sketches for equestrian statues, for vast tableaux, for intricate details of religious works. If Da Vinci started out wanting to, quite simply, complete a treatise on painting, it soon expanded into such huge associated byways – studies of light, water, mechanics and more - that the whole became unwieldy and was never completed. The layout of the drawings is often innovative too, with great thought gone in to page layout for drawings and writings that were to be part of any one of these treatises.

The history of the drawings, representing the private Leonardo, the excursions into science and anatomy, warfare and portraiture, is fascinating in itself. In 1519, on the artist's death, Da Vinci's assistant, Francesco Melzi, took the drawings back to his family home near Milan and spent the next 50 years organizing them by subject. When he died, sculptor Pompeo Leoni acquired these loose sheets and bound them in two (or more) huge leather volumes After his death, the larger volume containing technical drawings eventually ended up in the Biblioteca Ambrosiana in Milan. But the smaller volume of approximately 600 more artistic drawings ended up, by 1630, in England in the possession of the collector Thomas Howard, Earl of Arundel. In 1642, Howard fled England during the Civil War with part of the collection, but by 1663 (after the Restoration of the Monarchy) his grandson was showing off Da Vinci's drawings to castle guests at Christmas. By 1690, Charles II had acquired them – one can only imagine under what auspices – and all 600-odd drawings have since remained in the Royal Collection, removed from their binding under Queen Victoria to conserve them in what can now only be described as near-pristine condition. Arranged thematically in this Queens Gallery exhibition, they make for a fascinating few hours study.

Leonardo da Vinci: A Life in Drawing, Queens Gallery, Palace of Holyroodhouse, Canongate, Royal Mile, Edinburgh, 0303 123 7306 Until 15 Mar 2020 (closed 25-26 Dec), Daily, 9.30am – 4.30pm Adult £7.50/Under 17 £3.80, other concessions available

Don't miss

Since winning the Summerhall Prize at the annual Royal Scottish Academy Open Show, Will Knight, graduate of Glasgow School of Art, has been drawing the corridors and people of Edinburgh's Summerhall arts centre in what is an accurate but artistic survey of the building. Resident for the past year, Knight has taken a forensically-detailed approach to observation and recording of space and people, charting the nature of the organization in scale drawings. This weekend, you can also catch the venue's annual Christmas craft fair.

Some of Summerhall: A Survey in Drawings, Summerhall, 1 Summerhall, Edinburgh, Until 8 March 2020, Weds - Sun 11am - 6pm

Critic's Choice

Visual Arts Scotland and the Society of Scottish Artists this year mount a joint Christmas show at the RSA in Edinburgh for those who like their festive kicks a little less prescriptively festive. Amongst some 200 works of contemporary art and craft picked – and do bear in mind that there is much work on sale here too, should you have the wherewithal - from 2,200 submissions from the society's members and those further afield, is “Under Over: Over Under” from the Cordis Trust, the tapestry-centred organization set up by Miranda Harvey and Ian Rankin (yes, that one).

The works here have been chosen by curator Harvey from six different artists, all working in different ways with tapestry and the idea of tapestry, and with materials ranging from silk to lead, paper to wool. There is abstraction from Sue Lawty and geometry from Dali Behannah. Elizabeth Ashdown uses Passementerie techniques and Celia Pym darning, knitting and embroidery. Sarah Jane Henderson creates innovative surfaces working from research into the emotional health of young people, and Sahvi Jawah integrates tapestry-making and earth architecture techniques in an investigation into the topography of Bangalore. These are not works in traditional tapestry technique, but inspired by or constructed in a similar way to tapestry or weaving. Ideas are bound up in the threads, here, as they are in the abstract paintings, the conceptual installations, the assembled sculptures that will surround them in what promises to be a thought-provoking addition to the Trust's long-standing aim of celebrating Edinburgh as a centre of tapestry excellence and innovation, and a fascinating complement to the contemporary work of the VAS/SSA.

Under Over: Over Under, VAS/SSA Open, Royal Scottish Academy, The Mound, Edinburgh, or 22 Dec – 30 Jan 2020 (closed 25 and 26 Dec) Daily 10am – 5pm.