The Stockton and Darlington Railway (S&DR), which opened in 1825, was the world's first permanent steam locomotive public railway.

Overview
Inspired by wealthy local wool merchant Edward Pease, the S&DR was authorised by Parliament in 1821 and was initially intended to be an ordinary horse-drawn plateway, which were then commonplace in England. However, George Stephenson had been perfecting his engines at Killingworth for about seven years, and had built the Hetton colliery railway. With a deputation from Killingworth, he persuaded Edward Pease, on the day that the Act received Royal Assent, to allow him to resurvey the route and work it, at least partly, by steam.
Accordingly, a new Act of Parliament was obtained approving Stephenson's changes to the route, and a clause added to permit the use of "loco-motive or moveable engines". This latter clause narrowly escaped being struck out of the bill due to officials not understanding the meaning. The bill also included provisions for transporting passengers though, at the time, they were regarded as little more than a sideline.
He had given up on the "steam springs" that were proving unsuccessful at Hetton, but retained other improvements, such as the direct connection of the pistons by crank rods, though the wheels were coupled by gears. He also made improvements to the track to overcome the problems with settling of the stone blocks on which they were laid, and used T-section malleable iron in fifteen foot lengths, for the rails, pioneered by John Birkinshaw at Bedlington Ironworks in 1820.
Initially Stephenson's son Robert assisted him, but then went to join William James in surveying a proposed new line between Liverpool and Manchester. George and Robert, with Edward Pease and Michael Longridge (owner of Bedlington Ironworks) together set up a company at Newcastle-on-Tyne, to manufacture locomotives, which became Robert Stephenson and Company.
The line was twenty six miles in total, with two cable-worked inclines at the western end, joined by a short horse-worked section. From Shildon the line was relatively level through Darlington to Stockton. The line's structures included one of the first railway bridges. Designed by architect Ignatius Bonomi, the so-called 'first railway architect', the Skerne Bridge in Darlington is the oldest railway bridge still in use today. The bridge was also commemorated on the Bank of England five-pound note. SD&R's track gauge was required to accommodate the horse-drawn wagons used in the older wagonways serving coal mines. This influence appears to be the main reason that 1435 mm (4 ft 8½ in) was subsequently adopted as standard gauge.
Steam locomotives were then a new and unproven technology, and were slow, expensive and unreliable. The initial impetus for steam power had come during the Napoleonic Wars, when horse fodder had become very expensive, and had still not settled down, while improving transport and mining methods was making coal more plentiful. However, many people weren't convinced that steam engines were a viable alternative to the horse. So at first, horse traction predominated on the S&DR, until steam could prove its worth.
The first locomotive to run on the S&DR was Locomotion No 1, built at the Stephenson works though, in the absence of Robert, Timothy Hackworth had been brought in from Wylam. (On Robert's return he took charge of maintenance at the S&DR's Shildon's Soho works.) "Locomotion" used coupling rods rather than gears between the wheels, the first to do so.
The official opening of the line was on 27 September 1825; the first steam-hauled passenger train ran and carried up to 600 passengers. The first passenger train was not fast, taking two hours to complete the first 12 miles (19 km) of the journey. Most of the passengers sat in open coal wagons but one experimental passenger coach, resembling a wooden shed on wheels and called "The Experiment," carried various dignitaries.
An experimental regular passenger service was soon established, initially a horse-drawn coach with horse provided by the driver. While passenger carrying was contracted out, locomotive coal trains were either paid by the ton, contractors providing their own fuel, which meant they tended to use the cargo, or by fixed wages, which meant they did not bother to economise.
Three more engines were built similar to Locomotion then, in 1826, Stephenson introduced the "Experiment" with inclined cylinders, which meant that it could be mounted on springs. Originally four wheeled, it was modified for six. Not all engines came from Stephenson. In 1826 also, Wilson, Robert and Company, of Newcastle, produced one for the line which, rather than use coupling rods, had four cylinders, two to each pair of wheels. Possibly because of its unusual exhaust beat, it became known as Chittaprat. After suffering a collision it was not rebuilt. These early locomotives were slow and unreliable and Hackworth set out to produce an improved design and in 1827 introduced the Royal George, salvaging the boiler from the Wilson engine. He also invented a spring-loaded safety valve, because drivers had been tying them down to prevent them opening when the loco went over a bump.
Steam traction was expensive in comparison to horse drawn traffic, but it soon proved that it was viable and economic. Steam locomotives could haul more wagons, and haul them faster, so in a typical working day the expensive steam engine could haul more coal than the cheaper horse. It soon became apparent that mixing faster steam-hauled and slower horse-drawn traffic was slowing the operation down, and so as steam technology became more reliable, horse-drawn traffic was gradually abandoned.
At first, the organisation of the S&DR bore little relation to that of most modern railways, and was run in the traditional manner of the wagonways of the time. The S&DR merely owned the tracks and did not operate trains; anyone who paid the S&DR money could freely operate steam trains or horse-drawn wagonloads on the line. This separation of track from trains resembled the canals, where canal companies were often forbidden from operating any boats. There was no timetable or other form of central organisation. Trains ran whenever they wanted, and fights often broke out when rival operators came into conflict over right-of-way on the tracks.
This chaotic situation was tolerable on completely horse-drawn traffic wagonways, but with faster steam trains it soon became unworkable, as the faster speeds meant a collision could have serious consequences. With the advent of steam, new operating methods had to be developed.

See also

Pomeranz, Kenneth and Steven Topik (1999). The World That Trade Created: Society, Culture, and World Economy, 1400 to the Present. M.E. Sharpe, Inc., Armonk, NY. ISBN 0-7656-0250-4. 
Ransom, P.J.G., (1990) The Victorian Railway and How It Evolved, London: Heinemann.
Stretton, C.E., (1896) The Development of the Locomotive: A Popular History (1803-1896), London: Crosby, Lockwood and Son.