Explanation:

The word Peshwa is from Persian, meaning "foremost, leader". A Peshwa (Marathi: ????? / "Peshwe" / "Peshve") is the titular equivalent of a modern Prime Minister. Maratha ruler Shivaji created the Peshwa designation in order to more effectively delegate administrative duties during the growth of the Maratha Empire.
Here is the list of Appointed and Hereditary Peshwas -
Sr.    Name    Particulars    Reign Began C.E.    Reign Ended C.E.
1    Balaji Vishwanath    Assisted the Syed Brothers in deposing the Mughal Emperor Farrukhsiyar in 1719    17 November 1713    12 April 1720
2    Baji Rao I    Helped conquer Central India (Malwa) and Rajputana and extended his dominions into Gujarat in the northwest and Deccan in the south. Raided Mughal Delhi in 1738. He was the most powerful Peshwa. Here are few noted quotes about Baji Rao First -

"He died as he lived, in camp under canvas among his men, and he is remembered to this day among the Marathas as the fighting Peshwa and the incarnation of Hindu energy.” — Sir Richard Carnac Temple, Shivaji and the Rise of the Mahrattas

“Bajirao was a heaven born cavalry leader. In the long and distinguished galaxy of Peshwas, Bajirao was unequalled for the daring and originality of his genius and the volume and value of his achievements.” — Sir Jadunath Sarkar, foreword in V.G. Dighe's, Peshwa Bajirao I and Maratha Expansion    12 April 1720    28 April 1740
3    Balaji Bajirao    Managed to extend the Maratha territories into most of North-West, East and Central India. Lost the Third Battle of Panipat in 1761    28 April 1740    23 June 1761
4    Madhav-Rao I    Fraught with internal dissensions and successful Wars with the Nizam    23 June 1761    18 November 1772
5    Narayan-Rao    Assassinated by Gardi guards    18 November 1772    30 August 1773
6    Raghunath-Rao    Responsible for extending empire till Peshawar in North-West and also saw the decline of Maratha power in North India. Deposed by Nana Phadnis & 11 other administrators in what is now called "The Baarbhai Conspiracy"    1773    1774
7    Madhav-Rao II    Dominated by the political intrigues of Nana Phadnis. Saw the resurgence of Maratha power in North India.    1774    27 October 1795
8    Baji Rao II    1st Reign - Was defeated by Yashwantrao Holkar, ruler of Indore, at the Battle of Poona. Fled to British protection, and in December 1802, concluded the Treaty of Bassein with the British East India Company, ceding territory for the maintenance of a subsidiary force and agreeing to treaty with no other power. This provoked the Second Anglo-Maratha War that began the breakup of the Maratha confederacy.    1796    1802
9        2nd Reign - During his second reign began the Third Anglo-Maratha War. After the defeat at the Battle of Koregaon in January 1818, he was on the run from the British. Eventually, the British took over his dominion and made the Maratha King Pratap Singh of Satara declare in favour of the British and this ended the Peshwa's legal position as head of the Maratha confederacy. On 3 June 1818, Baji Rao surrendered to the British; he was banished to Bithur near Kanpur.    1803    1818
10    Nana Sahib    He was a leader during the Indian Uprising of 1857. As the adopted son of the exiled Maratha Peshwa Baji Rao II, he sought to restore the Maratha confederacy and the Peshwa tradition.    1851    1857