In 1829 Johann Wolfgang Dobereiner, German chemist, arranged elements into 3 number group with similar chemical properties and stated atomic mass of middle element is roughly the average of first and third elements atomic masses.
E.g. Salt formers: Chlorine (Cl) [35.5] ; Bromine (Bt)  ; Iodine (I) 
3. Newland's law of octaves
In 1865, British chemist, J.A.R. Newlands propsed that when elements are arranged in increasing order of atomic masses, every eighth element has similar physical and chemical properties of it's first element. He compared it to the law of octaves in music.
It is rejected as it is not applicable for the elements which atomic mass more than 40.
4. Lother's-Mayer's atomic volume curve
They plotted a graph between atomic volume and atomic mass of elements and noticed that similar elements took position at same points.
5. Mendeleev's periodic law
In 1869, Russian chemist, Dmitri Mendeleev arranged the elements known at the time in order of relative atomic mass along with few other changes.
Mendeleev is the "Father of periodic table".
In periodic table, horizontal rows = periods & vertical columns = groups.
There are 7 periods & 9 groups (I, II, III, IV, V, VI,.VII, VIII, ZERO).
6. Moseley's modern periodic law
In 1913, British chemist, Henry Moseley used atomic number instead of atomic mass.
It has 7 periods and 18 groups.
It is classified as 4 blocks.
S block - Alkali & alkaline earth metals.
P block - Chalcogen, picogens, halogens and inert gases.
D block - Transit elements.
F block - Inner transition elements.
Two horizontal rows at the bottom with 14 elements of a row. First row with atomic number from 58 to 71 called as Lanthanide series. Second row with atomic number from 90 to 103 called as Actinide series.