Granted, these days you can buy kitchen timers for a song, when they are not a free give-away with something – but it is nevertheless a nice finger exercise to put something like that together yourself, using parts that you probably have lying around somewhere.
The heart of the circuit is formed by a CD4060 (yes, an ‘antique’ CMOS IC) that contains an oscillator and a chain of series-connected flip-flips. The clock signal that is generated by the internal oscillator (a symmetrical square wave), is divided by two in the first stage (by the way, the output from this stage is not brought out of the IC), divided by 2 again in the second stage, and so on.
The result is that on output Q12 (refer to the schematic in Figure 1) there appears the oscillator signal divided by 212 = 4096, and on output Q13 the oscillator divided by 213 = 8192. When we make the oscillator frequency adjustable, our timer is actually done already.
This oscillator frequency is determined by the components to the left of the IC (C1 and R1 through R7) and is made selectable with S1. The network C2, C3 and R8 ensure that the timer is reset when the power supply voltage is switched on, so that all outputs (Q12 and Q13 included) are low. Depending on the position of S1, output Q12 will go high after 1, 3, 5, 7½, 30 or 45 minutes (when using the values as indicated in the schematic). With S2 you can double these times again by selecting output Q13.
Once Q12 or Q13 goes high, the self-oscillating buzzer Bz1 is switched on via transistor T1, which will then loudly announce that the selected time has elapsed. Instead if a buzzer you could also use a relay (but don't forget the free-wheeling diode!), and the circuit, of course, invites experimentation with various component values.
Finally: the CD4060 is, as already noted, relatively antique (although still available); but in the early days of this IC there was a Babylonian confusion of tongues about the naming of the outputs. In the original datasheet for the 4060 from TI, output Q13 (pin 3) has been labelled as ‘Q14’...