user78645: I am reading Andreas M. Antonopoulos's book and In chapter 10 - Assembling and Selecting Chains of Block he writes:

Under most circumstances this is also the chain [main chain] with the most block
  in it, unless there are two equal-length chains and one has more
  Proof-of-Work.

Can somebody explain how this is possible? How can 2 chains with the same length have different cummulative Proof-of-Work? Is it because they might include block that were mined with different difficulty targets? Not sure how this could happen, but this is my only hypothesis.

user63872: 
How can 2 chains with the same length have different cummulative Proof-of-Work? Is it because they might include block that were mined with different difficulty targets?

That is correct. The bitcoin protocol actually follows the chain with the highest accumulated proof-of-work, not the largest block height. 
I believe the original implementation followed the largest block height, but that left the network open to certain attacks, so it was soon changed to largest accumulated proof of work. 

78645: <p>I am reading <strong>Andreas M. Antonopoulos's</strong> book and In <strong>chapter 10</strong> - <em>Assembling and Selecting Chains of Block</em> he writes:</p>

<blockquote>
  <p>Under most circumstances this is also the chain [main chain] with the most block
  in it, unless there are two equal-length chains and one has more
  Proof-of-Work.</p>
</blockquote>

<p>Can somebody explain how this is possible? How can 2 chains with the same length have different cummulative Proof-of-Work? Is it because they might include block that were mined with different difficulty targets? Not sure how this could happen, but this is my only hypothesis.</p>
 63872: <blockquote>
  <p>How can 2 chains with the same length have different cummulative Proof-of-Work? Is it because they might include block that were mined with different difficulty targets?</p>
</blockquote>

<p>That is correct. The bitcoin protocol actually follows the chain with the highest accumulated proof-of-work, not the largest block height. </p>

<p>I believe the original implementation followed the largest block height, but that left the network open to certain attacks, so it was soon changed to largest accumulated proof of work. </p>
