It began as a cabinet of curiosities, a strange collection of botanical and ethnographical objects gathered together by two eminent gardeners, John Tradescant father and son, and put on public display in their house in Lambeth. Now, after years of tinkering and juggling with inadequate funding, it is reopening as a spacious repository of art and antiquities with a new mission of connecting cultures and civilisations for the better understanding of them by both students and the international public. The oldest public museum in the oldest university in the English speaking world has had a 21st century remake designed by the architect Rick Mather and costing £61m, to create an international facility for both students and public.

The Ashmolean first opened in Broad Street in 1683, the Tradescant collection having been passed on by the family to the scholar Elias Ashmole adding to his own, and eventually outgrew the building and moved in the 1840s to Beaumont Street to a neo-classical building designed by Charles Cockerell.

Only the galleries and facilities at the front of the old museum remain. The extensions behind the Cockerell building, completed in the 1890s, have been replaced by the new Mather designed open spaces, with natural light serving each of five levels from an atrium, and bridges linking them.

"It is" said Professor Andrew Hamilton, Oxford's new vice-chancellor "a powerful statement of the way in which Oxford's dynamic future is being fuelled by the richness of its past. Today, as a result of the effort, commitment and generosity of so many - and as part of the Campaign for Oxford - the special role of the Ashmolean has been secured for generations to come".

The museum is a teaching and research department of the University as well as being a public museum, for which admission is free. The Ashmolean has been completely recast to a strategy of "Crossing Cultures Crossing Time", said Christopher Brown, the museum's director. "From the outset, the ambition has been to create not just an improved and expanded version of Britain's oldest public Museum, but something significantly different in kind: a new way of showcasing the Ashmolean's remarkable collection, for the benefit of the wildest possible audience".

The Ashmolean's holdings are based on the idiosyncratic collections of the Tradescants, which was known as Tradescant's Ark. In the early 17th century the first John Tradescant travelled widely abroad and brought back not only plants but also other items which caught his imagination, as his son later also did. After the death of the second Tradescant the Ark objects were given to Ashmole who, with his own collections, bestowed on them the university. It included Guy Fawkes's lantern, the robe of the native king of Virginia, the hand of a mummy, and a stuffed dodo (which eventually became so moth-eaten it had to be destroyed).

The museum flourished as the collections grew including the acquisition of the Alfred Jewel in 1718, still one of the Ashmolean's most famous objects and in 1845 a neo-classical building was erected for it, and under the curatorship of Arthur Evans more galleries were added in 1894. They were notoriously dark, difficult to negotiate and had indifferent atmospheric conditions, so that they earned the nickname "The Evans Sheds". "I always felt they were fine if you had a professor of Aegean archaeology at your elbow, but 99% of people didn't so that it used to be difficult to understand their significance" said Brown.

The modern Ashmolean is a wide ranging repository of art and antiquities, now ranged across 39 galleries replacing 60% of the old museum and connected to give real and notional connections between cultures and styles. In the lower first floor galleries are many of the original Ashmolean objects, explained, and the museum's renowned large textile collection is shown nearby for the first time, including Lawrence of Arabia's robes which were left to the museum - none of it being on display before because of the inadequate environmental controls.

The Ashmolean has a re-eminent collection of Minoan artefacts, many corning from a 19th century excavation at Knossos, which can be properly seen for the first time, and the Islamic, Japanese and Chinese art are also shown in much greater depth than before. 

Fine art is also more comprehensively exhibited, with more space for portrait sculpture. Among the large paintings display is a Titian, The Triumph of Love, identified by the museum's experts after conservation. There is also a purpose-built education centre with its own entrance, four new temporary exhibition galleries, and a top floor restaurant with a terrace over-looking the city. Of the costs, £45m has now been raised with the university underwriting the remainder, but the project was at first made possible by a £15m grant from the Heritage Lottery Fund and £10m from the Linbury Trust, the personal charitable fund of Lord and Lady Sainsbury.