I was wondering why the elements in the periodic table were disposed the way they are. I understand, of course, that they are put in increasing atomic number fashion, but I'd like to know more about the topic. Could you link some reference that examine in detail the structure of the periodic table?
I do not address the question of history, of Mendeleyev's investigations, that is answered in How was Mendeleev able to develop his table?
Modern understanding of basic principles follows. Let us have a piece of periodic table
... A0 B0 ... ... A1 B1 ... .............
Element "B0" must have the next atomic number after "A0", i.e. one more electron. It is different chemically, although may have (albeit not necessarily) similar physical properties.
Element "A1" must be chemically similar to "A0", although physical properties may differ significantly (as a general rule, ".1" elements are denser than ".0"). It happens that for each element there exist its "analog" in the next period, that has similar chemical properties (based on similar outer-shell electron configuration). This pattern, once noticed, permitted for good predictions (search for Mendeleyev's "eka" elements in Internet for more information).
Periods have different lengths. Analog's atomic number may be 8, 18, or 32 ahead off the prototype's atomic number (the number of electrons expended to "raise" all the configuration one shell up). This difference is due to quantummechanical effects.
The vertical columns are families, which are elements that share similar characteristics. For example on the far right side of the periodic table are the alkali metals, known for being extremely reactive. and on the opposite side are the noble gases, which are known for reacting to very few substances. The horizontal periods are organized by the atomic number; the number of protons in an particle.
Dimitri Mendeleev purposely left spaces in the periodic table because he knew there were elements that had not yet been discovered, that would need a place on the periodic table.