How to compare earthquake magnitudes On the USGS website, it says


  Because of the logarithmic basis of the scale, each whole number
  increase in magnitude represents a tenfold increase in measured
  amplitude;


However my book says this:


  Like many other scales in science (decibel is another example), Richter scale is not linear. This means that an earthquake of magnitude 6 does not have one and half times the destructive energy of an earthquake of magnitude 4. In fact, an increase of 2 in magnitude means 1000 times more destructive energy. Therefore, an earthquake of magnitude 6 has thousand times more destructive energy than an earthquake of magnitude 4.


But based upon the USGS information, an increase in 2 magnitude would be 10 x 10 = 100 stronger.

Now which one is correct?
Taken straight-out from Prof. L. Braile's collection of earthquake hazard information, that explains it quite nicely:


  The magnitude scale is really comparing amplitudes of waves on a seismogram, not the STRENGTH (energy) of the earthquakes.


While one unit of magnitude is 10 times the amplitude on a seismogram, one unit of magnitude represents $10^{1.5}$ times (approximately 32 times) the energy, based on the long-standing empirical formula

$$\log{E} \propto 1.5M$$

thus

$$E \propto 10^{1.5M}$$

where $E$ is energy and $M$ is magnitude.

The example set in the webpage is to compare how much bigger would a 9.7 magnitude earthquake be in comparison to a 6.8 magnitude earthquake:


The magnitude scale is logarithmic, so a magnitude 9.7 earthquake is $\frac{10^{9.7}}{10^{6.8}} = 794.328$ times bigger on the seismogram than a magnitude 6.8 earthquake.
Measuring the change in energy, however, shows that the 9.7 earthquake is $\frac{{10^{1.5}}^{9.7}}{{10^{1.5}}^{6.8}} = 10^{1.5 \times (9.7-6.8)} = 22~387$ times the energy of a 6.8 earthquake.


Comparison of earthquake "size" on seismograms: this image from Nevada Seismological Lab's Living with Earthquakes in Nevada

A graphical comparison of earthquake energy release, a video by the US NWS Pacific Tsunami Warning Center (PTWC).

The USGS has a calculator for magnitude difference.

And there's a calculator for seismic energy and several equivalences. Unfortunately, most of the equivalences are related to the USA.

See Brian Hill's answer that explains that with the original Richter scale, one unit of magnitude is apprimately $31^{1}$ times the energy, and two units of magnitude are $31^{2}$ times the energy, and so on.

In short: you are half-right (one unit of magnitude it is 10 times bigger on the seismogram, not in energy), and the book is right (two units of magnitude are 1000 times stronger).