A transimpedance amplfier like George drew. A transconductance amplfier could be used, but usually they're pretty sloppy compared to a good op-amp in that configuration.

Another way would be to use a balancing Hall effect circuit- an amplifier produces a current, causing a magnetic field to cancel the field caused by the conductor in which you're measuring current.

All three methods can have arbitrarily small burden depending on how good your amplifier is. The first two require your circuitry to supply the entire current being measured, with the latter you can scale it by the ratio of turns in the measuring coil vs. the balancing coil (in other words, if you're trying to measure 100A with 1 turn, you could balance the field with 2000 turns and 50mA from the amplifier.

A transimpedance amplifier like George drew. A transconductance amplifier could be used, but usually they're pretty sloppy compared to a good op-amp in that configuration.

Another way would be to use a balancing Hall effect circuit- an amplifier produces a current, causing a magnetic field to cancel the field caused by the conductor in which you're measuring current.

All three methods can have arbitrarily small burden depending on how good your amplifier is. The first two require your circuitry to supply the entire current being measured, with the latter you can scale it by the ratio of turns in the measuring coil vs. the balancing coil (in other words, if you're trying to measure 100A with 1 turn, you could balance the field with 2000 turns and 50mA from the amplifier.