
In Distributed Algorithms, Nancy Lynch provides a blueprint for designing, implementing, and analyzing distributed algorithms. She directs her book at a wide audience, including students, programmers, system designers and researchers. Distributed Algorithms contains the most significant algorithms and impossibility results in the area, all in a simple automata-theoretic setting. The algorithms are proved correct, and their complexity is analyzed according to precisely defined complexity measures. The problems covered include resource allocation, communication, consensus among distributed processes, data consistency, deadlock detection, leader election, global snapshots, and many others. The material is organized according to the system model - first by the timing model and then by the interprocess communication mechanism. The material on system models is isolated in separate chapters for easy reference. The presentation is completely rigorous, yet is intuitive enough for immediate comprehension. This book familiarizes readers with important problems, algorithms, and impossibility results in the area: readers can then recognize the problems when they arise in practice, apply the algorithms to solve them, and use the impossibility results to determine whether problems are unsolvable. The book also provides readers with the basic mathematical tools for designing new algorithms and proving new impossibility results.
Security Engineering. Ross Anderson
The Formal Semantics of Programming Languages. Glynn Wynskell.
Communicating Sequential Processes. Tony Hoare. This book is surprising in its compactness and lucidity.
Pi Calculus. Robin Milner.
Semantics With Applications. Hanne Riis Nielson
On Concurrent Programming. Fred Schneider.
Specifying Systems with TLA+. Leslie Lamport.
Distributed Algorithms. Nancy Lynch.
Reliable Distributed Computing. Ken Birman and Robert Van Renesse.
I'm sure I'll recall more as soon as I hit "reply".
If you are just learning programming, plan on taking your time with the algorithms but practice coding every day. Find a fun project to attempt that is within your level of skill.
If you are a strong programmer in one language, find a book of algorithms using that language (some of the suggestions here in these comments are excellent). I list some of the books I like at the end of this comment.
If you are an experienced programmer, one algorithm per day is roughly doable. Especially so, because you are trying to learn one algorithm per day, not produce working, production level code for each algorithm each day.
Some algorithms are really families of algorithms and can take more than a day of study, hash based look up tables come to mind. First there are the hash functions themselves. That would be day one. Next there are several alternatives for storing entries in the hash table, e.g. open addressing vs chaining, days two and three. Then there are methods for handling collisions, linear probing, secondary hashing, etc.; that's day four. Finally there are important variations, perfect hashing, cuckoo hashing, robin hood hashing, and so forth; maybe another 5 days. Some languages are less appropriate for playing around and can make working with algorithms more difficult, instead of a couple of weeks this could easily take twice as long. After learning other methods of implementing fast lookups, its time to come back to hashing and understand when its appropriate and when alternatives are better and to understand how to combine methods for more sophisticated lookup methods.
I think you will be best served by modifying your goal a bit and saying that you will work on learning about algorithms every day and cover all of the material in a typical undergraduate course on the subject. It really is a fun branch of Computer Science.
A great starting point is Sedgewick's book/course, Algorithms [1]. For more depth and theory try [2], Cormen and Leiserson's excellent Introduction to Algorithms. Alternatively the theory is also covered by another book by Sedgewick, An Introduction to the Analysis of Algorithms [3]. A classic reference that goes far beyond these other books is of course Knuth [4], suitable for serious students of Computer Science less so as a book of recipes.
After these basics, there are books useful for special circumstances. If your goal is to be broadly and deeply familiar with Algorithms you will need to cover quite a bit of additional material.
Numerical methods -- Numerical Recipes 3rd Edition: The Art of Scientific Computing by Tuekolsky and Vetterling. I love this book. [5]
Randomized algorithms -- Randomized Algorithms by Motwani and Raghavan. [6], Probability and Computing: Randomized Algorithms and Probabilistic Analysis by Michael Mitzenmacher, [7]
Hard problems (like NP) -- Approximation Algorithms by Vazirani [8]. How to Solve It: Modern Heuristics by Michalewicz and Fogel. [9]
Data structures -- Advanced Data Structures by Brass. [10]
Functional programming -- Pearls of Functional Algorithm Design by Bird [11] and Purely Functional Data Structures by Okasaki [12].
Bit twiddling -- Hacker's Delight by Warren [13].
Distributed and parallel programming -- this material gets very hard so perhaps Distributed Algorithms by Lynch [14].
Machine learning and AI related algorithms -- Bishop's Pattern Recognition and Machine Learning [15] and Norvig's Artificial Intelligence: A Modern Approach [16]
These books will cover most of what a Ph.D. in CS might be expected to understand about algorithms. It will take years of study to work though all of them. After that, you will be reading about algorithms in journal publications (ACM and IEEE memberships are useful). For example, a recent, practical, and important development in hashing methods is called cuckoo hashing, and I don't believe that it appears in any of the books I've listed.
[1] Sedgewick, Algorithms, 2015. https://www.amazon.com/Algorithms-Fourth-Deluxe-24-Part-Lect...
[2] Cormen, et al., Introduction to Algorithms, 2009. https://www.amazon.com/s/ref=nb_sb_ss_i_1_15?url=search-alia...
[3] Sedgewick, An Introduction to the Analysis of Algorithms, 2013. https://www.amazon.com/Introduction-Analysis-Algorithms-2nd/...
[4] Knuth, The Art of Computer Programming, 2011. https://www.amazon.com/Computer-Programming-Volumes-1-4A-Box...
[5] Tuekolsky and Vetterling, Numerical Recipes 3rd Edition: The Art of Scientific Computing, 2007. https://www.amazon.com/Numerical-Recipes-3rd-Scientific-Comp...
[6] https://www.amazon.com/Randomized-Algorithms-Rajeev-Motwani/...
[7]https://www.amazon.com/gp/product/0521835402/ref=pd_sim_14_2...
[8] Vazirani, https://www.amazon.com/Approximation-Algorithms-Vijay-V-Vazi...
[9] Michalewicz and Fogel, https://www.amazon.com/How-Solve-Heuristics-Zbigniew-Michale...
[10] Brass, https://www.amazon.com/Advanced-Data-Structures-Peter-Brass/...
[11] Bird, https://www.amazon.com/Pearls-Functional-Algorithm-Design-Ri...
[12] Okasaki, https://www.amazon.com/Purely-Functional-Structures-Chris-Ok...
[13] Warren, https://www.amazon.com/Hackers-Delight-2nd-Henry-Warren/dp/0...
[14] Lynch, https://www.amazon.com/Distributed-Algorithms-Kaufmann-Manag...
[15] Bishop, https://www.amazon.com/Pattern-Recognition-Learning-Informat...
[16] Norvig, https://www.amazon.com/Artificial-Intelligence-Modern-Approa...
Absent a book, there are a lot of great resources online. High Scalability(http://highscalability.com/) has a good amount of quality links to distributed systems content, and some editorial content of varying quality. In general, it's a good site to follow if you're interested in how distributed systems are being used in industry. I also like to follow Aphyr's blog(http://aphyr.com/), Daniel Abadi's blog(http://dbmsmusings.blogspot.com/), and Henry Robinson's blog(http://the-paper-trail.org/blog/) and Peter Bailis's blog(http://www.bailis.org/).