The First Railway
Liverpool - Manchester
The first railway, at least the railway that started the railway revolution, was the railway between Liverpool and Manchester. The Liverpool and Manchester Railway was the first inter-city service. The line opened on the 15th of September 1830.
It is possible to claim that the Stockton - Darlington track should be classified as the first railway. It was opened on the 27th of September 1825, five years before the line between Liverpool and Manchester. While the 40 kilometer (26 miles) track had some of the features of a modern railway, it also had some features not associated with modern railways. Originally, it was meant to use horses to pull the wagons but George Stephenson also tried his steam powered locomotive on the track. The line also included two inclines with cables. The Stockton and Darlington railway owned the tracks but did not operate any trains. Anyone who paid could run locomotives or horse drawn wagons on the tracks. This meant there were no time tables and at times fights broke out when rival operators argued about right of way.
The success of the Liverpool - Manchester line was partially thanks to the lessons learnt from the Stockton - Darlington line. The 56 kilometer track (35 miles) between Liverpool and Manchester was made as level as possible, with three steep grades (maximum 2%). The engineer, George Stephenson, had learnt from the Stockton - Darlington line that even small inclines slowed down the early locomotives.

The train to Manchester at Liverpool Lime Street Station
The railway was double track from the beginning. The gauge, 1435 millimeter (4 feet 8.5 inches) was the same as Stockton Darlington and was to become the standard for most future railways. Since this was the first double track railway no one knew what the distance between the two tracks should be. Stephenson choose to use the same distance between the tracks as between the rails (1435 millimeter), partly to keep the cost of land purchases down. It was too narrow, it constrained the width of the trains and limited the safety of the passengers. Indeed, it contributed to the first death of a railway passenger.
The original track was not allowed to go into Liverpool, the track terminated at Crown street station and the length of the track was 31 miles. Just one mile longer than the crow flies. Not bad, given that some of the land owners had refused to cooperate with the railway. The drawback of the direct route was that it required a lot of expensive bridges and viaducts. And the track had to cross a swamp, Chat Moss. In 1836 the track was extended to Lime Street station in Liverpool.
Today, two car diesel trains make the journey between Liverpool Lime Street and Manchester Victoria in an hour, roughly twice as fast as back in the 1830's. The route has only bit slightly modified since the original from the 1830's. Unfortunately, the journey can not be classified as exciting in any way. Except for that this is the railway that started the railway era, completely changing the world.

A replica of a coach from 1829 at the National Railway Museum in York
Sadly, an accident occurred on the opening day. At the Parkside station, William Huskisson (a member of Parliament for Liverpool) got out and wanted to talk to the Prime Minister, Duke of Wellington. He was standing on the side of the Duke's carriage when the other engine, the Rocket, was passing by on the other track. Huskisson could have climbed into the carriage or taken refuge on the embankment. But he was clinging to the side of the duke's carriage. Had he stayed completely still, he would have been safe. But maybe he panicked or maybe his permanently damaged foot failed him. In any case, he got hit by the Rocket and his legs were crushed. He died a few hours later.
According to Matthew Engel, William Huskisson set the pattern for what virtually every British politicians would do from that day on when trying to make decisions about transport. He dithered, he panicked, he got it spectacularly wrong. Close to Newton-le-Willows station there is a memorial. The Parkside station, the scene of the accident, does not exist any longer. An impressive memorial was erected at the site which has recently been renovated to its former glory. But unless you know the exact location of the monument you are unlikely to notice it from the train. It is on the south side of the tracks.
Huskisson was the first railway passenger to be killed in an accident. But the first recorded death on the Liverpool - Manchester line happen already in 1827. One of the navvies (they who build the early railways) died while working on the tunnel on the approach to Liverpool. Many more deaths would follow, building railways in the 19th century was a dangerous job. Not helped by the fact that part of the wages was paid in beer!
Part of the track was used for the famous Rainhill test in October 1829, to decide what locomotives to use on the railway between Liverpool and Manchester. The winner was the Rocket built by George and Robert Stephenson. It averaged 14 miles per hour (12 mph according to some sources), achieving a top speed of 30 miles per hour.