Alphabetically :

Chemical Elements

A PG-rated French mnemonic   (about a  weird  family diner)  

K	Ho He!
L	Lili Becta Bien Chez Notre Oncle François-Nestor.
M	Napoléon Mangea Allègrement Six Poulets Sans Clamser Après.
N	Karl Carrément Scanda :  "Tirez-Vous, Craignez Mon Féroce Courroux...  Nichée Cupide, Zinzins Gâteux, Gérontes Assurément Séniles, Brigands Kremlinesques."
O	Rebecca Strangula Yvon Zircon... Nébuleuses Motivations  (Techniquement, "Rut Rhénan", Pardi) Agitant Cadavéreusement,  Indéniablement, Son Subconscient Tellement Idéologiquement Xénophobe.

For the Lanthanides  (elements 57-71)  see Martyn Poliakoff's video on Lanthanum:
Language Centers Praise Ned's Promise of Small European Garden Tubs.
Dinosaurs Hobble Erotically Thrumming Yellow Lutes.
("Thrumming" is for thullium.  Yellow is for ytterbium.)

An easier American mnemonic for the Lanthanides (elements 57-71) is:
Ladies Can't Put Nickels Properly [into] Slot-machines.
Every Girl Tries Daily, However, Every Time You Look.

  Main Classification :

The above grouping by column is supplemented by the important distinctions listed below.

Early textbooks (before the 1950's) were excluding groups 11 and 12 from the transition metals.  Elements of group 11 are now universally recognized as transition metals, so are elements of group 12 under the simple convention adopted here, following many modern authors who view  d-block  and  transition metals  as strictly synonymous.  The current definition from the IUPAC is controversial; it would classify Zinc and Cadmium as post-transition metals while Mercury  (and Copernicium)  should be considered transition metals, because of the recent (2007) synthesis of mercury tetrafluoride  (introducing a new oxidation state for Mercury that has been given a relativistic explanation which doesn't apply to Zinc or Cadmium).

Actinides are normally classified as  rare earths  because of their obvious chemical similarities with lanthanides, without the endorsement of the IUAPC  (this issue is relatively unimportant, because of the lack of chemical uses of actinides outside of nuclear engineering).

As the above table demonstrates, the franctic search for elements 85 and 87  (before WWII)  once left a few nomenclature debris.  It also left at least one textbook example of  pathological science  (perceived observations at the threshold of detectability that turn into pseudoscience).  The so-called  (imaginary)  Allisson effect  was advocated by  Fred C. Allison (1882-1974)  well beyond the call of scientific duty, even after his method was disproved by H.G. MacPherson  (of UC Berkeley)  in 1934...  A case worth studying.

The current official procedures for enacting the names of new elements were adopted well after the settlement (1997) of a major naming controversy  (the Transfermium War)  about elements 104, 105 and 106.

In 1997, element 109  (Meitnerium, Mt) was named after  Lise Meitner  (1878-1968).  The rare honor was widely perceived has some kind of posthumus apology for not having shared the Nobel prize  (Chemistry 1944)  awarded to  Otto Hahn  for their joint work.  This was also a way to honor the team as the name  Hahnium  (for element 105)  had to be permanently dropped to avoid further confusion after the  naming war.

On 19 February 2010  (the 537 ^th anniversary of Copernicus' birth)  element 112 was officially given the name that had been under review since July 2009:  Copernicium  (Cn).  Its temporary name in the IUPAC system was Ununbium (Uub).  Alternately, it can be identified as eka-mercury (or eka-hydrargyrum, eka-Hg) the same way element 111  (Roentgenium, Rg)  was formerly known as eka-gold.  Mendeleev himself introduced the prefix "eka-" to name any undiscovered element after whatever appears above it in the periodic table  (such elements are chemically similar).

Electronic Configurations :

The quantum state of an electron around a nucleus is fully described in terms of the following four  quantum numbers :

• The principal quantum number (n) determines the  shell.  In the absence of external fields, the  (negative)  energy  of a bound electron depends  only  on that number  (it's inversely proportional to  n² ). 
• The azimuthal quantum number (l) ranges from 0 to n-1 within a given shell and determines what's called a  subshell, normally designated by a traditional letter s (l=0), p (l=1), d (l=2) or f (l=3).

  Electrons per Subshell Subshell Maximum  s   0  2 p 1 6 d 2 10 f 3 14   L 2(2L+1)

  The etymology of these letters can be traced to the spectroscopic vocabulary predating quantum mechanics (s=sharp, p=principal, d=diffuse, f=fundamental).  A subshell is normally denoted by the number of the shell (n) followed by such a letter, yielding a designation like  ns, np, nd or nf  (e.g., "3d"). 
• The magnetic quantum number (m) ranges from -L to L within a given subshell and determines an  orbital, which may "contain" no more than two electrons of opposite  spins  (see next). 
• The spin of an electron is a two-valued quantum number (s = ±½).

The  Pauli Exclusion Principle  states that two electrons cannot be in the same quantum state.  They must differ in at least one of the values of the above 4 quantum numbers.  This implies that a subshell (n,l) may contain no more than 2(2l+1) electrons, as tabulated above  (the total number within the whole shell is at most 2n² ).

1s
2s          2p
3s          3p
4s      3d  4p
5s      4d  5p
6s  4f  5d  6p
7s  5f  6d  7p

The minimal energy of the electronic cloud surrounding a lone nucleus is achieved when electrons occupy available subshell room in the order at left, starting with the 1s subshell.  This simplified version of the  Aufbau principle  explains the structure of the periodic table of elements, where elements with similar chemical properties are listed in the same column:  The chemical properties of an element depend mostly on the  valence  electrons located in the outermost subshell(s) which are usually the least favored energetically  (with the reservations noted below, in the case of "f" subshells).

The electronic configuration around a nucleus may be summarized by listing all nonempty subshells in the above order of increasing energies (1s, 2s, 2p, 3s, etc.) with a superscript indicating the number of electrons in each.  The repartition of electrons into orbitals of the same subshell is usually ignored.

A complementary term symbol is sometimes added to better describe the ground configuration.  It may be obtained using Hund's Rule,  a set of empirical recipes due to Friedrich Hund (1896-1997).  Electrons avoid pairing up on the same orbital unless all the orbitals of the subshell are occupied.

For brevity, the configuration of a noble gas may be denoted by its bracketed symbol  [as a prefix]  in the electronic configuration of subsequent elements.  Note that all subshells of noble gases are full.  Chemical inertness is due to an outter shell containing a total of 8 electrons (except for helium).

In the periodic table, successive "transition metals" correspond to the "filling" of a "d" subshell (from 1 to 10 electrons).  Adding 1 to 14 electrons to the empty "f" subshell of Lanthanum yields the other elements of the Lanthanide series (Z = 58 to 71) whose chemical similarity with Lanthanum may be explained by stating that the "f" subshell corresponds to orbitals that are "closer" to the nucleus than those of the previous "s" subshell, so "f" electrons are less likely fo be valence electrons  (the same situation repeats with Actinium and the Actinides series, from Z = 89 to 103).  This geometrical explanation should not be taken too literally...

For completeness, it should be noted that the energy levels of some subshells are so close that the pairing of electrons may lead to a few exceptions  (in particular for Cr and Cu)  in the application of the simplified  Aufbau principle  presented above.

Geometric Designations of the Orbitals

N	L	M
		-2	-1	0	+1	+2
1	0			1s
2	0			2s
	1		2py	2pz	2px
3	0			3s
	1		3py	3pz	3px
	2	3d xy	3d yz	3d z2	3d xz	3d x2-y2

Theoretically, the chemistry of even highly radioactive heavy elements can be precisely computed from the well-known laws of quantum electrodynamics  (as if  radioactivity didn't exist).  In practice, such a computation is way beyond our current abilities and chemistry remains an experimental science...  Nevertheless, the ingenuity of experimentalists is considerable and some chemical facts have been obtain for an element like Hassium (Z = 108) although only about 40 atoms of it have ever been observed.  This is made possible by the fact that Hassium happens to have a surprisingly stable isotope  (Hs-277)  with a half-life of more than  10 minutes,  as explained in an excellent video interview of Martyn Poliakoff  (part of  The Periodic Table of Videos,  produced by  Brady Haran).