Get yourself to Ancoats, to the east of the city, on the far side of the Northern Quarter. Don’t take too long about it as it is changing before your very eyes, just as it has been doing these past two-and-a-half centuries. If you’re coming from Piccadilly station, it’s barely half a mile away; north up London Road, straight on along Piccadilly and, at the bottom right hand of the Gardens of that name, head right along Newton Street.

No great distance to walk but, in historical terms, the proverbial giant leap; if Manchester was the cradle of the Industrial Revolution, then Ancoats was a midwife. In the last decade of the 18th century, and the first two of the 19th, it changed from open farming land to a blackened grid of cramped streets, cotton mills and factories. “Mud below, smoke above,” was what met the author Thomas De Quincey’s eye when he came this way in 1821.

Even among the cleaned-up remnants of this teeming quarter, you can almost feel the weight of work, heavy as a bank of Lancashire rain clouds. In Redhill Street stands the great mass of Murrays’ Mills, now a quiet monument to the boom years of the cotton-spinning industry, but still daunting in its sheer bulk and uniformity. To walk this way is to sense the terrible majesty of the city’s manufacturing growth, a sheer cliff face of masonry to your left, the broad cut of the Rochdale Canal to your right. Not many English cities have such grand husks of industry quite so close to the core. A starker urban answer to the hills and rivers to the north you never did see.

Facebook Twitter Pinterest Murrays’ Mill on Redhill Street. Photograph: Alamy

Work your way north through Ancoats via Bengal Street or the parallel Radium Street; use the linking side roads of Naval, Loom, Silk or Primrose Streets. Linger rather than stride, look across the sudden fallow gaps, catch the old backs of the dwelling houses next to the clean cubes of their modern counterparts. At Oldham Road turn left. By heading east here, you are walking in the footsteps of those peaceable if angry marchers who came this way to hear orator Henry Hunt appeal for electoral reform in the gathering grounds of St Peter’s Field on one of the city’s, and the nation’s, most fateful days: 16 August 1819. We cannot help but come to that.

But first head down Tib Street, boasting the tavern of that name, one of Manchester’s most vaunted. Up Market Street and into the heroic if frankly disappointing Arndale Centre. Heroic because of its rising from the debris of the 1996 bombing by the IRA, the biggest such blast in Britain’s peacetime history; disappointing because of such blandness and brand uniformity on this scale. Pass through it and be relieved that it is as unMancunian as the strange vertical aberration and skyline vandal that is Beetham Tower. This is a mixed-use wafer of a thing: part hotel, part homes, the tallest non-London building in the UK, and an instrument of loud eerie sounds as the winds swirl through the glass blade of its ever-visible summit. Manchester groundlings wail bitterly about the noise, as if it is an emblem of unsought otherness.

Facebook Twitter Pinterest Tib Street Tavern. Photograph: Alamy

Right into Corporation Street, past the defiant anachronism of a Victorian pillar box, the only structure in the heart of the explosion to have survived intact. Letter-writers post their correspondence here for good luck. “This is how we used to make things,” it seems to say.

Just down to the west here, on Cross Street, is the magnificent Royal Exchange building. You can’t not go in. When it was built in 1809, it was said to house the largest room in the world, the centre of the global industry that gave rise to Manchester’s nickname: Cottonopolis. Quartered here was the empowering wealth being coined by Britain on the backs of – let’s be blunt, in this of all towns – slaves. The place is, of course, haunted.

Today, in its vast cubic metres of air, stands a theatre, no less. Bearing the name of the building, it stands there like a module just landed. While much seemingly solid Manchester stuff gets torn down and replaced, this peculiar thing went the other way; when it opened in 1976, it was temporary. Now, four decades of success have bestowed permanence on it. Heavens, people come from London to see the productions.

Facebook Twitter Pinterest Victorian mill conversion and in the background Beetham Tower. Photograph: Getty Images

Go along Corporation Street towards Angel Square, site of some of the slums which drew the outraged attention of Karl Marx and his patron Friedrich Engels in the middle of the 19th century. Something strange happens before you get there: it is called Manchester Cathedral. The two words sound mutually contradictory, a head-on collision between industrial and ecclesiastical, modern and ancient. The truth confirms your surprise. In this top left-hand corner of the city, Manchester goes medieval. As cathedrals go, this one’s an upstart. The status was only bestowed on it in 1847, before which time it was a mere, albeit handsome, parish church and, in the overpowering whole of Manchester, still looks just that: slightly scuffed and apologetic. Next door are the famous Chetham’s School of Music and Library, the latter being the oldest free public reference library in Britain. You can sit at the window seat in the alcove where Marx and Engels used to meet.

Head back south down Deansgate, then left into John Dalton Street and Princess Street for the mighty municipal gothic vision of Alfred Waterhouse’s 1877-completed Town Hall; take in the Manchester Art gallery on Mosley Street, where, in one of the upstairs galleries, you can discover the often ignored influence on LS Lowry of the French impressionist painter Adolphe Valette. While teaching in Manchester early in the 20th century, he impressed on his young Salford student the immense visual potential of the urban landscape. Just as Manchester imbued Lowry’s vision, so his paintings have surely informed our ways of seeing his town, in all its self-invention.

Right, via St Peter’s Square, in Peter Street, past the Victorian bulk of the The Midland Hotel and on to the city’s finest building; well, finest frontage. We have arrived at the facade of the old Free Trade Hall. In so doing we have also reached, as those marchers through Ancoats did, the place where Hunt had come to speak. For this was once St Peter’s Field. It was here that the notorious and far-reaching massacre of Peterloo took place, when 15 peopled were killed and several hundred injured by cavalry dispersing sections of a crowd of some 60,000. The name was an ironic reference to the Battle of Waterloo four years earlier.

Facebook Twitter Pinterest Manchester Cathedral. Photograph: Getty Images

In its latter years as the Free Trade Hall, restored after blitz damage, the place hosted concerts by everyone from Sir John Barbirolli’s Halle Orchestra to Johnny Rotten’s Sex Pistols. Ever a magnet for protest, it was also here in 1966 that a dissatisfied punter shouted, “Judas!” at the freshly electrified folk star Bob Dylan. Today, in Manchester’s endless dance of building usage, the place is now a four-star hotel. Still, without the things that happened here, you would not be reading this; or at least not in this paper, for it was two years after Peterloo, following the closure of Manchester Observer, that the Manchester Guardian was launched, not dropping the city’s name from its title until 1959.

With history ringing in your ears, head down Lower Mosley Street, then Albion Street, for the relative calm of Deansgate Locks, then east towards Piccadilly station with the city’s, and therefore much of the industrialised world’s, successive lines of transport – land, canal, rail – running along in parallel.