The Shulhan Aruch (O.H. 275:1) rules that it is forbidden to read by candle light, lest one tilt the light and cause it to burn even stronger, thereby transgressing the forbidden act of Mav’ir (igniting) on Shabbat. This applies even to candles that are very high up and are out of reach, since once the Sages enacted this rule, they applied it to all candle light without distinction. Furthermore, although the Sages ruled regarding oil candles, it applies to wax candles as well, since they too can be caused to burn stronger by tilting them.
Rabbi Ben Zion Abba Shaul (Or LeZion, ch. 18, § 18) entertains the possibility that the wax used nowadays is less susceptible to requiring tilting in order to burn better than that used in the times of the Gemara, and that it would therefore be permitted to read beside wax candles. He writes that there is no significant difference and that it is similarly forbidden to read near modern day wax candles. Nevertheless, candles made of paraffin produce a more stable light and thus one may read by their light. Indeed, the Mishna Berura (M.B., O.H. 275:4) writes that stearin candles, which are derived from animal fat, were common in those days and were permitted. Rabbi Ovadia Yosef (Halichot Olam, vol. III, pg. 47), on the other hand, writes that one may even read by a wax candle nowadays.
Rabbi Baruch Toledano (Kitzur Shulhan Aruch) discusses applying the enactment of the Sages to electric light since one reading by a light may come to turn it on or off, or in the case of a dimmer, dim or brighten the light. However, he writes that the original enactment involved the case of a candle which begins flickering and therefore there is a concern that one will tilt the candle to allow it to burn better. Electric lights are stable and are do not tend to flicker and thus the enactment does not extend to electricity.
Summary: One may read by the light of a paraffin candle on Shabbat. There is no issue with reading with electric lights on Shabbat.