Exploration and interest in Africa is nothing new.  Europe and Africa have been connected through the Mediterranian World since the times of the the Greeks and Egyptians. However, with the inventions and technology of the Industrial Revolution and other advancements like the Renaissance and Scientific Revolution, a re-emergence in Africa occurred.  The systematic exploration began with the Scottish explorer James Bruce
James Bruce (1730-1794)
For many explorers of Africa, the biggest prize was the knowledge of river systems.  The largest of these is the Nile River.  Bruce's goal was to find the source of the Nile River.  Bruce and his party started in 1768.  While in Ethiopia, Bruce was well received by the Ethiopian king.  Bruce was able to treat and stop an outbreak of small pox.  Bruce also assisted in several military campaigns on behalf of the king.  Because of this good fortune, Bruce was able to have one of the more pleasant expeditions.

Bruce explored the regions of Lake Tana, visiting Tissiat Falls.  Bruce called this the source of the Nile River.  He was wrong of course.  What he found was the source of hte Blue Nile.  The Blue Nile is the principal tributaru of the Nile River.  Bruce's explorations rekindled interest in Africa.  His findings were challenged by Dr. Samuel Johnson who led a new expedition.  Bruce's book, Travels to Discover the Source of the Nile (1790) became very popular.
Don't forget the exploration of Napoleon during his Egyptian campaign.  This too influenced Europeans to travel and study Egypt and it's history.  Also, it gave France a new foothold in the continent.
Sir Samuel White Baker (1821-1893)
Sir Samuel Baker was an Englishman who lived in the British colony of Mauritius in the Indian Ocean.  He was a man that traveled extensively.  He traveled to Turkey, Eastern Europe, and eventually Egypt.  By studying the silt of the Nile River, Baker and his partner concluded that the Nile originated in Ethiopia.  In 1862 he traveled through the Nubian Desert meeting up with James Grant and John Speke.  The group then set out in 1863 facing a load of problems; hostile locals, heavy rains, African chiefs and uncooperative porters.  After 2 1/2 years in East Africa and the Sudan; Baker reached the shores of Luta N'zige (Uganda)

Baker renamed Luta N'zige Lake Albert in honor of Prince Albert, husband of Queen Victoria.  Lake Albert is paired with Lake Victoria (guess who it was named after).  Samuel Baker returned to Egypt for the opening of the Suez Canal in 1869.  Baker and his wife were then commissioned to help organzie government in south-central Sudan.  Samuel Baker's explorations helped clarify geography in Africa for Europeans.  Sadly, the Bakers also helped stem the slave trade in the region too.
Richard Burton (1821-1890) and John Hanning Speke (1927-1864)
Burton was a well traveled man of the British Empire.  He was active in India including the countries of Pakistan and Afghanistan.  During his time, Burton was sent back to England because of the controversy of him being a spy.  Burton was a master of disguise; he was able to travel in Arabia as an Afghani doctor under the name of Mirza Abdullah.
In 1854 he was commissioned to explore the modern day country of Somalia.  Burton was able to again to use his Islamic identity to travel across the region unimpeded.  These skills made it possible for Burton to gain information for the British in various ways.  When Burton traveled with Speke they appeared to have more hardship, both were wounded by natives in an attack.  After his fatal attack, Burton left the region and helped serve in the Crimean War (1854-55).  Speke stayed in Africa resting.
In 1857 Burton and Speke were called upon to solve the mystery of the source of the Nile River.  The expedition started in 1857 on the Indian Ocean in present day Tanzania.  Burton wanted to take a new approach and search for the source from the east.  The party marched for 500 miles by following the route of Arab slave caravans.  While on this route, they were told of a great inland sea, which were actually 3 lakes.  The party reached the shores of Lake Tangayika.  More hardship comes upon the men.  Both explorers were stricken malaria and other ailments.  The men started to return to the coast in 1858.  Speke went back out discovering that Lake Victoria was the real source of the Nile River.
Speke and Burton then started a famous dispute about their findings.   Both promised to wait to announce their findings when both returned to England.  Burton arrived in England 2 weeks earlier than his partner.  Once Speke arrived in England, Burton already received and was credited for all of their findings in Africa.  Regardless, Burton’s findings ended the Nile question.  The hot debate between the 2 men inspired more exploration of Africa and the next 2 men David Livingstone and Henry Stanley.  Incidentally the way that these explorers determined if somewhere could be the source was the height about sea level. Speke argued that Lake Tanganyika couldn’t be the source because it was 10 ft higher above sea level than the Nile.
Explored the Zambezi River, and explored the Eastern and Central Africa.  Famous for missing for over 3 years, Henry Stanley famously quotes, “Dr. Livingstone I presume.”  Livingston wanted to become a medical missionary and started his work in China, but the Opium War of 1839-42 caused him to change his plans.  Under the suggestion of a friend he chose to help in Africa.  He arrives in Angola Bay in 1841.  Livingston established a missionary in northeastern South Africa, but by 1849 the Boers (Dutch Africans, or Afrikaners).  Livingston leaves once the Boers start enslaving and abusing the natives.  He crosses the Kalahari that same year.  In 1851 he finds the Zambezi River and is greeted by the local chief.  He observes the abuses of the central African Slave Trade.  His new goal was to help eliminate the slave trade and bring new commerce to the region.
Livingstone is the first European to see Victoria Falls.  The next 5 years he explored the Zambezi and Ruvuma Rivers.  He located Lake Mweru and Lake Bangweulu.  Livingstone’s courage and personality made him a type of mythical living legend.  It was reported that Livingstone was missing leading the New York Herald to send Henry Stanley to find him.  After 18 months of side projects Henry Stanley went to search for David Livingstone.  Livingstone was easily found.  Livingstone never believed he was missing.  Once found Stanley stayed on to further explore. Stanley was known as the African natives as Bula Matari because of his brutal determination. Stanley’s further explorations located the source of the Congo River.  King Leopold used this information for the nation of Belgium.  Livingston’s contributions revealed that the interior of the continent was not a arid wasteland and rich in resources.
In 1875 less than 1/10 of Africa was under European control.  In 1895 less than 1/10 of Africa was independent of European control.  The exploration, missionary work, and romanticism encourage Europe to become more and more interested in the mysteries of Africa.
David Livingstone (1813-1873)
Sir Henry Morton Stanley (1841-1904)