I believe modern history began around the late 15th century, specifically in 1492 with Columbus's voyage to the Americas. This period marks the start of globalization and the rise of European powers in trade and exploration. Key developments like the Protestant Reformation and the Enlightenment further shaped modern thought, governance, and society, laying the groundwork for the contemporary world.
I guess it's fine if we start with the date given by Md. Rakib
But, what about Africa or South Africa, for example? I am thinking about the time the whites arrived. But that should be ancient history. Modern history for South Africa should be maybe 1994, but I am more than willing to give an earlier date.
Lungile Sojini makes a very valid point - Eastern, Western, First and Third World cultures will have varying definitions. Is the 'Modern Era' marked by changes in ideas, communication, social/political structures, travel or something else? For me, in Western History, the modern era has its roots in the development of the 1450 Guttenberg Printing press - the ability for more people to access information underpins the acceleration of changes socially, politically, and in religious ideas. Particularly when printed texts were in everyday language, so anyone who could read was able to access them.
Considering other areas of the world I am less sure - India, Africa, the East. A major issue is how to judge Modern - are we really talking about industrialization or just a way to chunk history into more manageable pieces - Pre History Ancient, Mediaeval, Renaissance/ Early Modern, Modern?
In my opinion, I would say roughly 1450-1500. This period marks the beginning of the age of exploration, the rise of nation-states in Europe, the invention of the printing press, and the start of the Renaissance. This is a common starting point for many introductory modern history courses.