Johannes Kepler first suggested that the gravitational pull of
the moon was the primary force behind fluctuations in sea level
in 1609. In 1616 Galileo described tidal fluctuations as the the
result of the earths rotation around the sun, rejecting Kepler's
hypothesis. In Isaac Newton's "Principia" he wrote a relatively
accurate description of tidal forces, but didn't take into
account continental bathymetry (shape of continents under the
ocean's surface). While the first adventures into explaining
this incredible phenomenon were relatively elementary, it set
the precedence that using the basic principles of physics to
describe earth's physical phenomenons is a very real
possibility.
It wasn't until the late eighteenth century that more accurate
equations came about from Pierre-Simon Laplace. Laplace was the
first one to factor in friction, resonance, and shape in the
continental crust into his observations. The development of
fluid dynamic equations resulted in Laplace developing equations
that more accurately predicted tides.
With modern remote sensing techniques and advanced modeling
methods, we are able to predict tides and measure their impacts
on coastlines and a wide variety of other phenomena that results
from tidal forces. Photos: Wikipedia