1. Earliest binding/cementing materials

The simplest, and possibly the earliest, binding material used was wet mud, and there are records of its use in ancient Egypt. Another example of a binder from the distant past is the use of naturally occurring bitumen by the Babylonians and Assyrians in their brick and alabaster (gypsum plaster) constructions.

Ancient Egyptians also used Calcined impure Gypsum.  

Early Greeks & Romans mostly used cementing material obtained by burning Limestone. Roman mortar was very hard & superior due to thorough mixing & long continuous ramming.

Lime is often considered as the "First Cement” of the mankind.

2. Naturally obtained Hydraulic Cement

Hydraulic Cement: Around 1000 BC, the ancient Greeks were the first to learn the beneficial effects of mixing lime with fine volcanic ash (may be, as a result of some lucky accident).

Ash can be thought of as naturally calcined rock, having silicon in a chemically active state like the calcium in calcined limestone.

When this lime-ash mixture is slaked, a whole new substance viz. calcium silicate hydrate ( i.e  C-S-H : approximately SiCa₂O₄ · xH₂O) is formed. C-S-H is an amorphous gel without any set crystalline structure. It hardens fast, even in water. And it is more durable than lime cement.

The ancient Greeks used this cement in a variety of ways. Some concrete cisterns built in that period survive to this day.

Later Greeks & Romans used volcanic ash & tuff mixed with lime & sand. Roman engineers mastered the technology and constructed seaports, aqueducts and temples of concrete as well. Some of these structures are as good as ever today, two thousand years later. The formula for Roman cement was not improved upon until the development of Portland cement in the early 1800s.

3. Earliest manmade cement (called Hydraulic Cement)

There was a general decline in the quality & use of cement in Middle ages. Advancement in the knowledge of cements could really take place only in 18^th century. In mid-eighteenth century, an English engineer named John Smeaton needed a strong material to rebuild the Eddystone lighthouse (shown in the picture on your right ) off the coast of Devon. He needed a hydraulic mortar that would set and develop some strength in the twelve hour period between successive high tides.

Smeaton concluded after investigations that lime-stone which contained considerable proportion of clayey matter yielded better lime possessing superior hydraulic properties. Thus was born, in 1756, the earliest manmade cement, called hydraulic cement. This was made by calcining nodules of argillaceous lime-stones.

However, it can not be called as an entirely new discovery. In fact, it was well known to builders in the earliest historic times that certain limes would, when set, resist the action of water, i.e. were hydraulic. It was also known that this property could be conferred on ordinary lime by admixture of siliceous materials such as pozzolana.

4. Roman Cement?

"Roman cement" was developed by James Parker in the 1780s, and finally patented in 1796.

It was, in fact, nothing like any material used by the Romans, but was a “Natural cement" made by burning septaria - nodules that are found in certain clay deposits, and that contain both clay minerals and calcium carbonate. The burnt nodules were ground to a fine powder. This product, made into a mortar with sand, set in 5-15 minutes.
The success of "Roman Cement" led other manufacturers to develop rival products by burning artificial mixtures of clay and chalk.

5. Artificial cement

Apparently unaware of Smeaton's work, the same principle was identified by Louis Vicat in the first decade of the nineteenth century. Vicat went on to devise a method of combining chalk and clay into an intimate mixture, and, burning this, produced an "Artificial Cement" in 1817.

6. British cement

Artificial cement was produced in 1817 by Louis Vicat by burning an intimate mixture of Chalk & Clay. 

Around the same time, James Frost, working in Britain, produced what he called "British Cement" in a manner similar to that for Artificial Cement, but did not obtain a patent until 1822.

7. Portland Cement

Joseph Aspdin is credited with invention of “Portland Cement” which he got patented in 1824.  

It was manufactured by mixing & grinding hard lime stones and finely divided clay into form of slurry & then calcining it in a furnace. 

8. Modern Portland Cement

Hydraulic limes, "Natural" cements and "Artificial" cements all relied upon their Belite content for strength development. Belite develops strength slowly. They contained no Alite (which is responsible for early strength in modern cements) because they were burned at temperatures below 1250 °C.

Thus these suffered from two major disadvantages:

1.  Fast-setting : this gave  insufficient time for placement

2.  Low early strengths: this required a delay of many weeks before formwork could be removed.

The first cement to consistently contain Alite was that made by Joseph Aspdin's son William Aspdin in the early 1840s. This was what we call today "Modern Portland Cement".

Because of the air of mystery with which William Aspdin surrounded his product, others (e.g. Vicat and 
I C Johnson) have claimed precedence in this invention, but recent analysis of both his concrete and raw cement have shown that William Aspdin's product made at Northfleet, Kent was a true Alite-based cement.

However, Aspdin's methods were "rule-of-thumb": Vicat is responsible for establishing the chemical basis of these cements, and Johnson established the importance of sintering the mix in the kiln.

However manufacturing cost of William Aspdin's product was considerably high & as such, his product was not received very well by the cement manufacturers of that time. But the product set reasonably slowly and developed strength quickly.
 

Slowly a market opened up for its use in concrete. The use of concrete in construction grew rapidly from 1850 onwards, and was soon the dominant use for cements. Thus Portland cement began its predominant role.