Let's start from the basic. What is algorithm? Formal definition can be found in text book and maybe will cited in wikipedia. For me algorithm can be explained as follow:

Algorithm = Recipes

Recipe is step by step definition to cook food. Same with algorithm, step by step definition to solve problems. But different with recipe which usually executed by human being, algorithm is executed by computer. Recipe can be written in free way and most of time can be understand by executor without to much problem. In the other side algorithm have to be precise in definition without any ambiguity so computer can executed that correctly. Later probably I want to write in more detail with popular way some post about fundamental algorithm.

In the mean time let's going back again to the discussion about the book. This book list following high level algorithm:

  1. Search Engine Indexing
  2. PageRank
  3. Public Key Cryptography
  4. Error-Correcting Codes
  5. Pattern Recognition
  6. Data Compression
  7. Databases
  8. Digital Signature
  9. Computability

The content of the book is delivered with very easy to understand way. I skip reading number one and two because I have read many books about google and Apache Lucene with more and less already explaining basic thing about search engine indexing and PageRank. Public Key Cryptography is an awesome chapter. It describe about Public Key Cryptography using very good analogy. Error-Correcting Codes and Pattern recognition raise my interest again to artificial intelligence  Data compression is delivered with detail description. I skip chapter database and continue to Digital Signature. Digital signature have some similarity with Public Key Cryptography. Digital Signature is one of chapter that took my interest a lot. Digital Signature is a method about how we can sign something and make sure our signature will be not tampered by someone. Last part actually not discussing any specific algorithm but more elaborating a question about is it any thing that can be computed by computer? 
The book is so concise and can be finished reading around 3 hours cumulative reading. Very recommended. Another expectation, I plan to write something relate to Cryptography and Digital Signature.