Human-computer interaction is a growing research area. There are several ways of interaction with the computer. Handwriting has continued to persist as a means of communication and recording information in the day to day life even with the introduction of new technologies. Due to the growth of technology in India, it becomes important to devise ways that allow people to communicate with computer in Indian languages. Hindi being the national language of India, we present a way to communicate with the computer in Hindi or more precisely, ‘Devanagari script’. Due to absence of a global font to represent Devanagari characters, it is important that the computer recognises the characters written by the user in order to interact with him. The algorithm implemented for character recognition first segments the image containing Devanagari text fed to the software into lines, lines to words and words to characters. The obtained characters are then brought down to a standard size. The Kohonen Neural Network based recogniser then comes into action and recognises the text character by character and provides the output in Unicode format. The network has been designed with no hidden layer to support quick recognition. Apart from text recognition from an image, we also provided the option to recognise individual handwritten characters drawn using a mouse. Such a system provides keyboard less computer interaction. The technique is implemented using Java. The overall recognition rate for a fixed font machine printed characters is 90.26% and for hand written characters, it is 83.33%.