Each of the three best known ancient generals (Alexander, Hannibal, Caesar) had rivers to cross. Hannibal had the Ebro in northern Iberia, Caesar had his famous Rubicon, and Alexander had the Granicus.
Rivers form natural boundaries and are relatively easy to defend, hence their importance in both modern and ancient warfare. The Persians were well aware Alexander was a skilled general and that his army was accustomed to victory, and that both were heading their way.
The Persians assembled a sizeable force to oppose Alexander's crossing, including Greek mercenaries (foot soldiers). Persia's own foot soldiers were a bit rubbish, but their cavalry was pretty good. Weirdly, it was the cavalry (which included Persian nobility) which gathered upon the banks to try and prevent the incursion.
Alexander, as was his wont, attacked at once, leading the charge of the Companions personally. His life was saved by Cleitus the Black, who severed the arm of a Persian noble who would otherwise have slain Alexander and dramatically altered the course of history.
The Persian cavalry retreated, leaving the Greek mercenaries to be cut to ribbons by Alexander.
As this happened quite a while ago, there are some disputes about precisely what happened, but the above is a reasonable outline. Once Alexander had crossed the Granicus, Asia Minor lay open to him. But, Darius, the Great King of Persia, commanded a huge number of men and plentiful resources.
Hellespont to the Granicus 50 - completed
The Granicus to Sardis 180 – 6/180
Sardis to Smyrna and back again 100
Sardis to Ephesus 50
Ephesus to Miletus 60
Miletus to Halicarnassus 60
Halicarnassus to Telmessus 160
Telmessus to Phaselis 160
Phaselis to Side 85
Side to Termessus 85
Termessus to Sagalassus 70
Sagalassus to Celaenae 60
Celaenae to Gordium 170
Gordium to Ancyra 80
Ancyra to Tarsus 320
Tarsus to Rugged Cilicia and back again 160
Tarsus to Myriandrus 100
Myriandrus to Issues 25
Total = 1,955