Group - Instead of grouping the elements according to the alphabetical order it is more sensible to group elements, in vertical columns, according to their chemical behavior. Usually elements will have rather similar chemical behavior, or there is an identifiable trend of certain physical properties within a group. The notable exception being the hydrogen atom which is unique and does not belong to any group. It is common to place it on top of the Group 1 elements. Some tables place it on its own that shows no clear affiliation with any other groups. Below listed some of the Group properties.
Group 1: Alkali metals - Chemically very reactive, soft metals. All react with water, giving off hydrogen gas. The reactivity trend increases for elements moving down the group. The melting point and boiling point decrease when moving down the group.
Group 7: Halogens - All members are non-metal and very reactive. The chemical reactivity trend decreases when moving down the group. They all react with hydrogen, producing gases which form acid solutions when dissolve in water. All elements in gas form are colored and the melting point and boiling point increase when moving down the group.
Group 0: Noble gas - Generally unreactive gases, do not found in earth's crust but found in the atmosphere in elemental forms (that is, do not form molecules but exist as single atom entities(monoatomic)). Chemical reactivity increases when moving down the group but then the compounds are generally unstable.
Transition metals - Between Group 2 and Group 3 there is a series of subgroups sandwiched in between (shaded in orange background). These elements are called the transition metals. They are so-called because, for a given hoizontal row, the filling of electrons occur at a similar electron orbital. They share some of the common chemical and physical characteristics across the horizontal row. For example, they generally have high melting point and form a variety of colored compounds.
Lanthanides and Actinides - These metals are grouped due to their similarity of chemical behavior. These metals (especially those of lanthanides) usually associate with one another in mineral ores. They are very difficult to extract and separate from one another. Consequently, it was once thought that they are rare and hence the name 'rare earths' which are still used until today.