Kelvingrove Art Gallery and Museum

Stand still for a moment and listen. Footsteps echo off polished stone floors. Voices rise and soften under a high, arched ceiling. Somewhere above you, light falls through tall windows onto warm red sandstone. The air feels cool, and it carries the faint smell of old wood and floor polish. This is Kelvingrove Art Gallery and Museum, and on most days it feels less like a hushed temple of art and more like Glasgow's own front room.

The building opened in 1901, as part of the Glasgow International Exhibition held in the park around you. At that time Glasgow called itself the Second City of the Empire. Its shipyards, engineering works and trade had made it very wealthy. The city wanted a palace for art and science, and it built one. The architects were John W. Simpson and E. J. Milner Allen, two Londoners who won a design competition.

Look at the exterior and you will see why people stop on the path to stare. The stone is a deep red sandstone from Locharbriggs, a quarry in Dumfriesshire in the south of Scotland. The style takes much from Spanish Baroque, a dramatic, highly decorated manner of building from seventeenth-century Spain. There are towers, turrets, carved figures and heavy ornament everywhere. In the soft Glasgow light, the stone can look almost pink. After rain, it turns the colour of dark rust.

Now for a story every Glaswegian seems to know. Legend has it that the building was put up back to front. People say the grand entrance should have faced Argyle Street, the busy road behind it. According to the tale, the architect was so upset by the mistake that he threw himself from one of the towers. It is a dramatic story — and it is not true. The main entrance was always meant to face Kelvingrove Park, where the exhibition crowds would arrive.

Step into the Centre Hall and look up. The space rises high above you, with galleries on either side and great arched windows. At one end stands a large pipe organ. It was built for the 1901 exhibition and later found a permanent home here. The museum still holds regular organ recitals. When the organ plays, the sound fills every corner of the hall. People on the upper balconies lean over the railings to watch and listen.

This hall gives you a clue about Kelvingrove's character. Many big museums separate art from natural history. Here, they share the same roof and sometimes the same room. Paintings hang near animal specimens. Armour stands not far from Egyptian objects. The mix was a deliberate choice when the galleries were redesigned. The museum closed for a major refurbishment in the early 2000s and reopened in 2006, with displays arranged around stories rather than strict categories.

Head into the West Court and you will meet one of the strangest sights in any museum. A Spitfire fighter plane hangs from the ceiling, its wings spread above the visitors. Below it stands Sir Roger, an Asian elephant. Sir Roger once lived in a Glasgow menagerie, and after he died around 1900 he was preserved and put on display. Children usually find him first. Adults often look up at the plane and simply say, "Why is that here?"

The answer is that Kelvingrove likes to surprise you. Cross to the East Court and you will see another example. Dozens of white heads hang in the air at different heights, each one with a different expression. Some smile, some frown, some look shocked. This installation is called Floating Heads, by the artist Sophie Cave. It is playful and a little unsettling. Walk slowly underneath and watch how the faces seem to change as your angle changes.

Now to the painting that many people come here to see. It is Christ of Saint John of the Cross, by the Spanish surrealist Salvador Dalí. The image shows Christ on the cross, seen from high above, floating over a dark sky and a calm bay. The city bought it in 1952. At the time many people thought the decision was a mistake. Today it is one of the most loved paintings in Scotland.

The painting has a troubled past too. In 1961, a visitor attacked it and tore the canvas. Restorers repaired the damage carefully, and today most people cannot see where it happened. Stand at the far end of the room before you walk closer. From a distance, the figure seems to hang in space. Up close, look at the small fishing boat and the figures on the shore. Dalí painted them with great precision.

Kelvingrove also holds a remarkable collection of European art. There are Dutch and Flemish paintings, French Impressionist works, and a painting by Rembrandt called A Man in Armour. But do not miss the Scottish rooms. Look for the Glasgow Boys, a group of painters from the late nineteenth century who brought fresh light and everyday life into Scottish painting. There is also a gallery for Charles Rennie Mackintosh and the Glasgow Style, the city's own version of decorative modern design.

The Mackintosh displays deserve a slow look. Mackintosh was a Glasgow architect and designer, famous for tall, narrow chairs, stylised roses and clean lines. Here you can see furniture, metalwork and designs by him and by artists around him, including Margaret Macdonald. These objects show a different Glasgow from the grand stone halls outside. Where the building is heavy and ornate, this work is light, elegant and almost quiet. The contrast tells you how quickly taste changed in only a few decades.

When you finally step back outside, turn around once more. The red towers rise against the sky. Across the park, on the hill, you can see the Gothic tower of the University of Glasgow. The River Kelvin runs below, through the trees. Families walk dogs, students cross the grass, and someone is probably eating a sandwich on a bench. Kelvingrove was built to impress the world... but it has become something simpler. It is a place Glaswegians come back to, again and again, just to wander.