The Horizontal Rows are named PERIODS
The Vertical Columns are named GROUPS.
The two most left - hand columns , Groups 1 & 2 are also known as the 'Alkali Metals' and 'Alkaline Earth Metals', respectively.
The two most right - hand columns , are Groups 17 & 18 and are known as the 'Halogens' and 'Noble/Inert Gases', respectively.
Groups 4 to 11 are often referred to as the Transition elements and produce coloured ions.
In Periods 6 & 7 are the Lanthanide and Actinide elements respectively. They are often shown as a separate block at the bottom of the modern Periodic Table. They lie between Groups 2 & 4. The Actinides are so-called because they contain all the Radio-ACTIVE elements.
Have a look at the 'Chemical Galaxy' on the 'web'. It shows all the elements in the form of a Catherine wheel. The spokes being the Groups and the circles being the Periods. It is quite spectacular and probably a truer representation of the elemental arrangements.
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