[<< wikibooks] General Chemistry/Properties of elements are periodic
The periodic table of the chemical elements is a display of known chemical elements, arranged by electron structure so that many chemical property|chemical properties vary regularly across the table.
The original table was created without a knowledge of the inner structure of atom|atoms: if one orders the elements by atomic mass, and then plots certain other properties against atomic mass, one sees an undulation or periodicity to these properties as a function of atomic mass.
The first to recognize these regularities was the German chemist Johann Wolfgang Döbereiner who, in 1829, noticed a number of triads of similar elements:

This was followed by the English chemist John Alexander Reina Newlands, who in 1865 noticed that the elements of similar type recurred at intervals of eight, which he likened to the octave|octaves of music, though his law of octaves was ridiculed by his contemporaries. Finally, in 1869, the German Lothar Meyer and the Russian chemist Dmitry Ivanovich Mendeleev  almost simultaneously developed the first periodic table, arranging the elements by mass. However, Mendeleev plotted a few elements out of strict mass sequence in order to make a better match to the properties of their neighbours in the table, corrected mistakes in the values of several atomic masses, and predicted the existence and properties of a few new elements in the empty cells of his table. Mendeleev was later vindicated by the discovery of the electronic structure of the elements in the late 19th century|19th and early 20th century.
Lists of the elements List of elements by name|by name, List of elements by symbol|by symbol, and List of elements by number|by atomic number are available.
The following figure shows the currently known periodic table of the elements.
Each element is listed by its atomic number and chemical symbol.
Elements in the same column ("periodic table group|group") are chemically similar.

Colour coding for atomic numbers:

Elements numbered in blue are liquids at room temperature;
those in green are gases at room temperature;
those in black are solid at room temperature;
those in red are synthetic and do not occur naturally (all are solid at room temperature).
those in gray have not yet been discovered (they also have muted fill colors indicating the likely chemical series they would fall under).The number of electron shell|electron shells an atom has determines what period it belongs to.  Each shell is divided into different subshells,
which as atomic number increases are filled in roughly this order:

2s           2p
3s           3p
4s        3d 4p
5s        4d 5p
6s     4f 5d 6p
7s     5f 6d 7p
8s  5g 6f 7d 8p

Hence the structure of the table.  Since the outermost electrons determine chemical properties, those tend to be similar within groups. Elements adjacent to one another within a group have similar physical properties, despite their significant differences in mass. Elements adjacent to one another within a period have similar mass but different properties.
For example, very near to nitrogen (N) in the second period of the chart are carbon (C) and oxygen (O).
Despite their similarities in mass (they differ by only a few atomic mass units), they have extremely different properties, as can be seen by looking at their allotrope|allotropes:  diatomic oxygen is a gas that supports burning, diatomic nitrogen is a gas that does not support burning, and carbon is a solid which can be burnt (yes, diamond|diamonds can be burnt!).
In contrast, very near to chlorine (Cl) in the next-to-last group in the chart (the halogen|halogens) are fluorine (F) and bromine (Br).
Despite their dramatic differences in mass within the group, their allotropes have very similar properties:
They are all highly corrosion|corrosive (meaning they combine readily with metal|metals to form metal halide salt|salts); chlorine and fluorine are gases, while bromine is a very low-boiling liquid; chlorine and bromine at least are highly colored.