The properties of the elements are a periodic function of their atomic numbers

Vertical columns are called groups or families.     Horizontal rows are called periods.

Group IA - Alkali Metals
Group IIA - Alkaline Earth Metals
Group VIIA - Halogens
Group VIIIA - Nobel Gases

Groups IA --> VIIIA   Representative Elements

Groups IB --> VIIIB   Transition Elements

Elements 58 --> 70      Lanthanide Elements

Elements 90 --> 102    Actinide Element

The Lanthanides and Actinides are both called Inner Transition Elements
 

An electron configuration indicates how electrons fill into subshells of a given atom. A "ground state" electron configuration illustrates electrons occupying the lowest available energy levels.

The sequence of subshell filling in not as straight forward as one might expect. Subshells in a given shell do not all always fill before some electrons are filled into the next higher shell.

The order of filling for electrons in a ground state electron configuration is illustrated by the Aufbau (German, to build) diagram.

Sample Electron Configuration

H 1s¹
Li 1s²2s¹
Na 1s²2s²2p⁶3s¹
K 1s²2s²2p⁶3s²3p⁶4s¹
Rb 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s¹

Na 1s²2s²2p⁶3s¹
Mg 1s²2s²2p⁶3s²
Al 1s²2s²2p⁶3s²3p¹
Si 1s²2s²2p⁶3s²3p²
P 1s²2s²2p⁶3s²3p³
S 1s²2s²2p⁶3s²3p⁴
Cl 1s²2s²2p⁶3s²3p⁵
Ar 1s²2s²2p⁶3s²3p⁶

K 1s²2s²2p⁶3s²3p⁶4s¹
Ca 1s²2s²2p⁶3s²3p⁶4s²
Sc 1s²2s²2p⁶3s²3p⁶4s²3d¹
Ti 1s²2s²2p⁶3s²3p⁶4s²3d²
V 1s²2s²2p⁶3s²3p⁶4s²3d³
 

Hund's Rule
When electrons occupy orbitals of equal energy (same shell and subshell) they fill into the subshell remaining unpaired to the maximum extent possible with their spins paired.
 

p⁴
 

Px Py Pz

d⁴
 

d⁷
 

A diamagnetic atom has no unpaired electrons and is slightly repelled by a magnetic field. A paramagnetic atom has at least one unpaired electron and is slightly attracted by a magnetic field. Ferromagnetism is a stronger form of paramagnetism.

One can observe that elements with similar chemistry, placed in groups by Mendeleev, have similar outer shell electron configuration.

Regularly repeating chemical properties, as observed in the Periodic Law, are a result of regularly repeating similar electron configurations.

The distinguishing electron for an element in the last electron added when following the Aufbau principle.

Electron configuration with f sublevels.
₆₄Gd 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d¹⁰5p⁶6s²4f⁸

Short hand for electron configurations using the noble gas in the previous period.
Ne 1s²2s²2p⁶
P 1s²2s²2p⁶3s²3p³
P [Ne] 3s²3p³
Ar 1s²2s²2p⁶3s²3p⁶
Ti [Ar] 4s²3d²

In general metals have good thermal and electrical conductivity, are malleable, lustrous, ductile and form positive ions. Nonmetals tend to opposite properties.

Metalloids have properties intermediate between metals and nonmetals. For example Si, Ge, Sb, are useful for making semiconductors.