These books are listed to be as updated as possible with current studies, and present a one-stop shop launchpad to current research, and will be listed in order of accessibility, meaning higher up -> easier to read.
(Subject/Issue | Book)
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Philosophy (including Logic):
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An atheist's take on the history of (Western) philosophy (this one in particular is notorious for its bias) | A History of Western Philosophy - Bertrand Russel (1945)
A Jesuit's take on history of philosophy (A true classic that tries to show the philosophy in detail and with as little bias as possible) | A History of Western Philosophy - Frederick C. Copleston (completed in mid 1970s)
Succinct general history and critiques of Western philosophy with their crucial flaws from a Christian standpoint | A History of Western Philosophy and Theology - John Frame (2015)
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An accessible take on the impossibility/trade-off of self-referentiality | Gödel, Escher, Bach: an Eternal Golden Braid - Douglas Hofstadter (1979)
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A compilation of Van Til's covenantal/presupposition-exposing style apologetics | Van Til's Apologetic: Readings and Analysis - Greg Bahnsen (1998)
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Math:
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Physics:
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A really accessible textbook on Quantum Field Theory | Quantum Field Theory for the Gifted Amateur - Tom Lancaster and Stephen J. Blundell (2014)
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General Challenges to atheism (including fine tuning, chemical coincidences etc.) | Modern Physics and Ancient Faith - Stephen M. Barr (2003; Catholic)
How physicists try to solve infinite regression and fine tuning without God: Inflation Theory (inflaton field) and String Theory | The Cosmic Landscape: String Theory and the Illusion of Intelligent Design - Leonard Susskind (2005)
Popular treatment on the latest physical theories (interestingly admits that the question of why there is something rather than nothing is not yet explained, yet finds solace in the fact that much of the universe can be explained by something that weighs less than a pet dog combined with inflation theory; good case study for the irrationality of physicists, since beginning problem is still left untreated) | The Fabric of the Cosmos: Space, Time, and the Texture of Reality - Brian Greene (2007)
Failure of the above to explain the universe (still doesn't explain beginning problem, is non-falsifiable, "explains anything anybody want" etc.)| Physics to God Website (run by two rabbis)
Basic Observation: Physicists rely on the inflaton field as the (unproved, and maybe unprovable!) theory to compensate for the low probability of this universe happening (which they readily concede) by taking out a theory that is too "strong" that allows them to say that anything that can ever happen will virtually happen (every universe will be substantiated in the megaverse that encloses them). The most obvious example is that Boltzmann brains, which is a more probable scenario in a universe that allows anything provided that the probabilities are high, are considered more "ordinary" within anthropic constraints, and therefore should be taken as the more likely scenario that our universe is in. This means that all of our memories are very likely false thanks to probability. Probability comes back to bite us.
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Chemistry:
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Trying to explain how everything came about at the chemical level, including life (particularly, abiogenesis is just speculated to have occurred on asteroids) | Chemical Evolution: Origins of the Elements, Molecules, and Living Systems (1991)
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Biology:
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A comprehensive book for Intelligent Design debates, philosophy of science etc. (interestingly, even talks about the inflaton field!) | Signature in the Cell: DNA and the Evidence for Intelligent Design - Stephen Meyer (2009) (The website for the book, on which you can find praises/critiques of the book up until 2012)